1) Which of the following are quadratic equation:
1) x²- 6x+4=0. Y
2) 2x²-7x= 0. Y
3) x+ 3/x=x². N
4) x²+ 1/x²= 2. N
5) x²+ 2√x - 3= 0. N
6) 3x²- 4x + 2= 2x²-2x+4. Y
7) x²+6x -4= 0. Y
8) √3 x²-2x +1/2 = 0. Y
9) x²+ 1/x² = 5. N
10) x - 3/x = x². N
11) 2x²- √3 x +9 = 0. N
12) x²-2x - √x 5 = 0. N
13) 3x²-5x +9= x²-7x +3. Y
14) x+ 1/x - 1= 0. Y
15) x²-3x = 0. Y
16) (x+ 1/x)² = 3(x +1/x) +4. N
17) (2x+1)(3x +2)= 6(x-1)(x-2). N
18) x²= x + 1/x, x≠ 0. Y
20) x² - 5x +3=0. yes
21) 3x²- 2= 0. Yes
23) x + 7/x = x². No
24) x³ + 1/ x³ = 2. No
25) x² + 4x -7√x + 4= 0. No
26) 2x²- 3x + 1=0. Yes
27) 7y² - 3y-5=0. Yes
28) z³ - 5z + z -2=0. No
29) 2x - 3/x = 4x². Yes
30) 5y²- 3y = 5. Yes
31) 2x = 3. No
32) 2y²+ 3/y² =5. No
33) x² + √2 x - 4=0. Yes
EXERCISE -B
1) In each of the following determine whether the given values are solution of the given equation or not
1) x²- x +1= 0; x=1. N
2) x²- x +1= 0; x=-1. N
3) x²- 3x +2= 0; x= 2. Y
4) x²- 3x +2= 0; x= -1. N
5) x²+ x +1= 0; x= 0. N
6) x²+ x +1= 0; x= 1. N
7) x² - 6x +5=0; at x=5
8) x² - 6x +5=0; at x= -1
9) 2x²- x +9 = x²+ 4x +3= 0; x= 2 y
10) 2x²- x +9 = x²+ 4x +3= 0; x= 3. Y
11) 2x² - 5x +3=0 ; 1/2
12) 2x² - 5x +3=0 ; 3/2.
13) 3x²- 2x -1= 0; x=1. Y
14) 3x²- 2x -5=0; x= 5/3
15) 3x²- 2x -5=0; x= 1
16) 6x² -x - 2=0; x= -1/2. Y
17) 6x² -x - 2=0; x= 2/3. N
18) 6x² - 11x +3=0; x= 3/2
19) 6x² - 11x +3=0; x= 1/3
20) 9x² - 3x - 2=0; x= -1/3
21) 9x² - 3x - 2=0; x= 2/3
22) x+ 1/x = 13/6 ; x=5/6. N
23) x+ 1/x = 13/6 ; x= 4/3. N
24) a²x²- 3abx + 2b²= 0; x= a/b. N
25) a²x²- 3abx + 2b²= 0; x= b/a y
26) a(x²+1)=x(a +1); x= a
27) a(x²+1)=x(a +1); x=1/a
28) a(x²+1)=x(a +1); x= -a
29) x²+√2 x -4= 0; x=√2. Y
30) x²+√2 x -4= 0; x= -2√2. Y
31) x² - 3√3 x +6 = 0; x=√3. Y
32) x²-3√3 x +6= 0; x= -2√3. N
33) x²- √2 x -4 =0; x= -√2. Y
34) x²- √2 x -4 =0; x= - 2√2. N
35) x²+ √2 x - 4=0; x= √2, x= -2√2
36) √7x² -6x - 13√7=0;x=13/√7, x=-√7
37)√(x²-4x+3)+√(x²-9)=√(4x²-14x+16); at x= 3
EXERCISE - C
1) In each of the following, determine the value of k for which the given value is a solution of the equation.
a) kx²+2 x -3= 0; x=2. -1/4
b) 3x²+2kx -3= 0; x=-1/2. 9/4
c) x²+2ax -k= 0; x=-a. -a²
d) 7x²+ kx - 3= 0; x= 2/3
e) x²- x(a+ b) + k= 0; x= a ab
f) kx² + √2 x -4= 0; x= √2. 1
g) x²- 3ax + k= 0; x= - a. 2a²
h) 3x² +2kx -3= 0; x=-1/2. -9/4
2) If x=2 and x= 3 are the roots of the equation 3x²-2kx +2m= 0; find the value of k and m. 15/2, 9
3) If one of the roots of the 2x²+kx - 6= 0 is 2. Find the value of k. Also, find the other root. -1, -3/2
4) If x=2/3 and x= -3 are the roots of the equation ax²+7x +b= 0; find the value of a and b. 3, -6
5) Determine, if 3 is a root of the equation √(x²- 4x +3)+ √(x²- 9)= √(4x²- 14x +16). No
6) If k+2= 0 is the factor of 4k²+ kp²+82=0. Find p. ±7
7) If 2k-1= 0 is the factor of k²+ 7kp² + 2p =0. Find p. -1/4
EXERCISE - D
Type -1
** Solve by factorisation method:
1) (x-4)(x+2)=0. 4, -2
2) (2x +3)(3x-7)=0. -3/2, 7/3
3) 4x² + 5x=0. 0, -5/4
4) 2x² -5x= 0 0,5/2
5) 4x² -25 =0 ±5/2
6) x² -9 = 0. +3,-3
Type -2
1) x² -8x +16= 0. ±4
2) x² +6x +5= 0. -1,-5
3) x² +9x - 52 = 0. 4,-13
4) x² - 2x -15= 0. 5,-3
5) x² - 11x +30= 0. 5,6
6) x² - 2x -48= 0. 8,-6
7) (x- 8)(x+4)= 13.
8) x² - 8x +15 = 0. 3,5
9) x² + 3x - 18 = 0. -5,3
10) x² - 3x -10 = 0. 5,-2
11) (x+3)(x-3)=40. ±7
12) 6+ x = x². 3,-2
13) x(2x+5) = 25. 5/2,-5
14) x(2x+5) = 3.
15) (x -4)² +5²= 13². -8,16
16) (x - 1/2)² = 4. 5/2, -3/2
17) x² - 11ax +28a²= 0. 4a, 7a
Type -3
1) 2x² +2 =5x. 1/2, 2
2) 2x² - 3x + 1= 0. 1,1/2
3) 2x² +7x + 6= 0. -2,-3/2
4) 2x² + ax - a² = 0. -a, a/2
5) 2x² - 3x +1 = 0. 1, 1/2
6( (2x+3)(x-4)=6. 9/2,-2
7) ax² +(a+b)x +b = 0. -1,-b/a
8) x² - (a+ b)x +ab = 0. a, b
9) 3x² - 14x -5= 0. 5,-1/3
10) 3x² +14x +8 = 0. -4,-2/4
11) 3x² -4x - 4 = 0. 2,-2/3
12) 3x² - 4x +1 = 0. 1, 1/3
13) 3x² = -11x - 10. -5/3,-2
14) 3x² = 2x +8. 2,-4/3
15) 3(x²-4)= 5x. 3,-4/3
16) 4x² +15= 16x. 5/2,3/2
17) 4x² +4x + 1= 0. -1/2,-1/2
18) 4x² -2x + 1/4= 0. 1/4,1/4
19) 5x² -3x -2= 0. -2/5, 1
20) 6x² -x -2= 0. 2/3,-1/2
21) 6x² +12x +3= 0. -3/3,-1/3
22) 6x² +5x - 4= 0. -1/2,-4/3
23) 6x² + x - 1= 0. -1/2,1/3
24) 6x² + x -15 = 0.
25) 6x² - x - 2 = 0.
26) (3x+1)(2x+3)= 3. 0, -11/2
27) 7x² = - 10x +8. -2,4/7
28) 8x² -22x -21= 0. 7/2,-3/4
29) 9x² -3x -2= 0. 2/3,-1/3
30) 9x² +6x +1= 0. ±1/3
31) 9x² + 15x -14 = 0.
32) 21x² = 4(2x+1). 2/3,-2/7
33) 48x² - 13x - 1= 0. -1/16, 1/3
34) 3a²x² + 2abx - b² = 0. b/3a, -b/a
EXERCISE- E
1) x(x+1)+ (x +2)(x+3)=42. 3,-6
2) 6x(3x-7)= 7(7- 3x). (7/3,-7/6)
3) a²x² -3abx + 2b² = 0. 2b/a,b/a
4) ax² +(4a²-3b)x - 12ab = 0. 3b/a, -4a
5) 25x(x +1)= -4 -4/5,-1/5
EXERCISE - F
1) 2x - 1/x = 1. -1/2,1
2) 10x - 1/x = 3 1/2,-1/5
3) 2/x² - 5/x +2= 0 2, 1/2
4) 2x²/3 - x/3 -1= 0. -1,3/2
EXERCISE - G
1) x² + 2√2 x -6= 0. -3√2,√2
2) x² -4√2 x +6= 0. √2,3√2
3) √3 x² +10x +7√3 = 0. -√3,-7/√3
4) 4√3 x² +5x -2√3 = 0. √3/4,-2/√3
5) √2 x² -3x -2√2 = 0. -1/√2, 2√2
6) x² -(√2 +1)x +√2 = 0. √2, 1
7) x²-(√3+1)x +√3 = 0. √3, 1
8) x² - (1+ √2)x +√2 = 0. √2, 1
EXERCISE - H
1) (x+3)/(x+2) = (3x-7)/(2x-3). -1,5
2) (x+2)/(x+3) = (2x-3)/(3x-7). 5,-1
3) (5x+1)/(7x+5)= (3x+1)/(7x+1). 1,-2/7
4) (3x-7)/(2x-5) = (x+1)/(x-1). 3,4
5) (x+3)/(x-1) = (2x+1)/(3x-5). -7,2
6) (x-1)/(x+1) = (2x-5)/(3x-7). 4,3
EXERCISE - I
1) x + 1/x = 5/2. 2,1/2
2) 3x - 8/x =2. 2,-4/3
3) x/3 + 9/x =4. 2,-4/3
4) x + 1/x = 626/25. 25, 1/25
5) mx²/n + n/m = 1- 2x. -(n±√(mn))/m
6) 7x + 3/x = 178/5. 5, 3/35
EXERCISE -J
1) 6x +29= 5/x. -5,1/6
2) 4/x - 3 = 5/(2x+3). -2,1
3) 1/(x-2)+ 2/(x-1) = 6/x, 3, 4/3
4) 1/(x +2)+ 1/x = 3/4. 2, -4/3
5) 6/(x+1) + 5/(2x+1) = 3. 2,-2/3
6) 8/(x+3)- 3/(2-x) = 2. 5, -1/2
7) 4/(x-1) - 5/(x+2) = 3/x. 3,-1/2
8) 5/(x-2) -4/x = 3/(x+6). 12,-2
10) 11/(5x-4) - 10/(4- 5x) = 1. 5, 4/5
EXERCISE - K
1) x/(x+1)+ (x+1)/x = 34/15, x≠0,x≠-1. 3/2,-5/2
2) x/(x+1)+ (x+1)/x = 13/6. 2,-3
3) x/(x-1) + (x-1)/x = 5/2. -1,2
4) 2x/(x -4)+ (2x-5)/(x -3)= 25/3. 6,40/13
EXERCISE - L
1) (x+3)/(x-2) - (1- x)/x = 17/4. 4,-2/9
2) (x+2)/6 - 1/(x+2) = 6. 1, -4
3) (x+1)/(x-1)- (x-1)/(x+1) = 5/6, x≠±1. 5,-1/5
4) (x-1)/(2x+1)+ (2x+1)/(x-1) = 5/2, x≠-1/2,1. -1
5) (x+1)/(x-2) + (x+11)/(x+3)=4. 5,-1/2
6) (x-1)/(x-2) + (x-3)/(x-4)=13. 5,5/2
Exercise - M
1) (x-3)/(x+3) - (x+3)/(x -3) = 48/7, x≠ ±3. 4,9/4
2) (x-a)/(x- b) + (x- b)/(x -a) = a/b + b/a. 0, a+ b
3) 2x/(x-3)+ 1/(2x+3) + (3x+9)/{(x-3)(2x+3) = 0. -1
EXERCISE - N
1) x² - 2ax + a²- b² = 0. a± b
2) x² - 4ax + 4a²- b² = 0. 2a± b
3) 4x² - 4ax + (a²- b²) = 0. (a± b)/2
4) 4x² + 4bx - (a²- b²) = 0. -(a+ b)/2, (a-b)/2
5) 4x² - 4a²x + (a⁴- b⁴) = 0. (a²± b²)/2
6) x²+ 2ab = (2a+ b)x. 2a, b
7) (a+ b)²x² - 4abx -(a - b)²=0. 1, -{(a- b)/(a+ b)}²
8) a(x²+1)- x(a²+1)= 0. a, 1/a
9) x² - x - a(a+1)= 0. -a, a+1
10) x²+ (a 1/a)x + 1 = 0. -a, -1/a
EXERCISE- O
1) 4x² - 2(a²+ b²)x + a²b² = 0. a²/2, b²/2
2) 9x² - 9(a+ b)x + (2a²+ 5ab +2b²)= 0. (2a+b)/3, (a+2b)/3
3) x² + {a/(a+ b) + (a+b)/b)x + 1 = 0. -a/(a+ b), -(a+b)/a
4) x² + x -(a+1)(a+ 2) = 0. -(a+2), a+1
5) x² + 3x -(a²+a - 2) = 0. -(a+2), a-1
EXERCISE - P
1) 1/(a+ b+ x) = 1/a + 1/b + 1/x, (a+b)≠0. -a, -b
2) 1/{(x-1)(x-2)} + 1/{(x-2)(x -3)}+ 1/{(x-3)(x-4)} = 1/6. -2,7
3) a/(x -a) + b/(x - b) = 2c/(x - c). 0, (2ab - bc - ac)/(a+b-2c)
EXERCISE - Q
1) (x -3)(x -4)= 34/33². 98/33, 133/33
2) (x -5)(x -6)= 25/24². 145/24, 119/24
**Solve by (SHREEDHARACHARY'S RULE)
EXERCISE - R
1) x²-17x = 84. 21,-4
2) (x+6)(x+4) = 120, 6,-16
3) x + 2/x +5= 0. -2,-1/2
4) x² - 26x²+ 25=0. 1,25
5) x² - 10x²+9=0. 1,9
6) x²- 13x²+ 36=0. 4,9
7) x - 2√x - 6= 0. 8±2√7
8) {x/(x+1)}²+6 -5{x/(x+1)}= 0,x≠ -1. -3/2, -2
9) 2{x/(x+1)}² -5{x/(x+1)}+2=0, x≠-1. -2, 1
10) {x/(x -1)}² -3{x/(x -1)} -18 = 0, x ≠1. 6/5, 3/4
11) {x/(x+1)}² + 5{x/(x+1)} +6=0, x≠-1. -2/3, -3/4
12) {2x/(x-5)}²+{10x/(x-5)} - 24=0, x≠5. 15, 4
13) 2x - 3/x= 1. 3/2, -1
14) y - 3/y = 1/2. 2, -3/2
15) 3y + 5/16y = 2. 5/12,1/4
16) 2(x²+ 1/x²) - 3(x + 1/x) - 1=0; x≠0. 2, 1/2
17) 3(x² + 1/x²) - 16(x + 1/x) + 26=0. 3, 1/3
18) (x+ 1/x)² - 4 + 3/2(x + 1/x) = 0 ;x≠0. 2, -1/2
19) 4(x² + 1/x²) - 4(x + 1/x) - 7=0; x≠0. 2, 1/2
20) (2x-3)/(x-1) - 4{(x-1)/(2x -3)}=3, x≠1, x≠3/2. 1/2, 4/3
21) {(3x+1)/(x+1)} + {(x+1)/(3x+1)} = 5/2, x≠-1, x≠-1/3
22) {(2x +3)/(x+1) + 6{(x+1)/(2x+3)} =7, x≠-1, x≠-3/2. -3/4, -2
23) 3√(x/5) + 3√(5/x) = 10, x≠0. 45, 5/9
24) √{x/(x-3)} + √{(x - 3)/x}= 5/2 ; x≠3, x≠0. 4, -1
25) (x +1)(x +2)(x+3)(x +4)= 120. -6,1
26) (x+2)(x - 5)(x - 6)(x +1)= 144. 7, -3/2
27) 1/(x+1) + 2/(x+2) = 4/(x +4), x≠ -1,-2,-4. (2+ 2√3)
28) (x-1)/(x+2) + (x- 3)/(x -4)= 10/3, x≠ -2,4. (1+√297)/4
29) p²x² +(p²- q²)x - q²= 0. -1, q²/p²
30) abx² +(b²- ac)x - bc= 0. c/b, -b/a
31) 9x² -9(a+ b)x +(2a²+ 5ab + 2b²)= 0. (2a+b)/3, (a+2b)/3
32) √(25- x²) = x - 1. 4
33) √x + 2x = 1. 1/4
34) √(217 - x) = x - 7. 21
35) √(2x +3) - √(x+1) = 1. 3, -1
36) √(3x +10) + √(6 -x)= 6. 2,5
37) √(2x+9) - √(x - 4)=3. 8, 20
EXERCISE- S
*** Write the discriminant of the following:
1) x² +2x +4= 0. -12
2) x² - x +1= 0. -3
3) x² - 4x +2= 0. 8
4) x² - 4x +a= 0. 16-4a
5) x² - 4x +1=0. 12
6) x² +x +1= 0. -3
7) x² - 2x +k= 0, k belongs to R. 4-4k
8) x² +px +2q= 0. p²- 8q
9) 2x² - 5x +3= 0. 1
10) (x - 1)(2x -1)= 0. 1
11) 3x² +2x -1= 0. 16
12) √3x² +2√2 x -2√3= 0. 32
13) 4x²- ax +2=0. a² - 32
EXERCISE - T
*** Determine the nature of the roots of the following:
1) x² - 4x +4= 0. Real, equal
2) x² +x +1= 0. Imaginary
3) x² - 5x - 7 =0. Real, distinct
4) x²+5x +5=0. Real, distinct
5) x²+2x +4=0. Imaginary
6) x² +2√3 x -1 = 0. Real, distinct
7) (x - 1)(2x -5) = 0. Real, distinct
8) (x - 2a)(x -2b)= 4ab. Real, distinct
9) 2x² + x -1= 0. Real, distinct
10) 2x² + 5x +5= 0. Imaginary
11) 2x² - 3x +4= 0. Imaginary
12) 2x²+ 5√3 x +6=0. Real, distinct
13) 2x²- 7x +6=0. Real, distinct
14) 3x²/5 - 2x/3 +1= 0. Real, distinct
15) 3x² - 2√6 x +2= 0. Real, equal
16) 3x²- 6x +5=0. Imaginary
17) 3x² + 2√5 - 5=0.
18) 4 - 11x = 3x². Real, distinct
19) 4x² - 4x +1= 0. Real, equal
29) 6x² + x - 2= 0. Real, distinct
21) 2(a²+ b²)x² +2(a+ b)x +1= 0. Imaginary
22) 9a²b²x² - 24abcdx + 16c²d²= 0. a≠ 0, b≠0. Real, equal
23) (b+ c)x² - (a+ b+ c)x +a= 0. Real, unequal
24) 4x² +12x +9=0. Real, distinct, -3/2, -3/2
25) √7 x² - 6x -13√7=0.
26) x²-54x +629=0.
27) 5x² - 19x+17=0.
28) √3 x² + 10x - 8√3=0.
29) 2x²- 2√6 x +3=0.
30) 3a²x²+ 8abx + 4b²=0 , a≠0.
31) 2x²+0.3x - 0.35=0.
EXERCISE - U
** Determine whether the following equation have real roots and if so, find the roots:
1) x² +x +2= 0. Imaginary
2) x² - 2x +1= 0. 1
3) x² +5x +5= 0. (-5-√5)/2
4) 3x² - 2x +2= 0. Not real
5) 6x² + x - 2= 0. -2/3
6) 9x² +7x -2= 0. -1
7) 16x² - 24x -1= 0. (3±√10)/4
8) 25x² + 20x +7= 0. Not real
9) 2x² - 2√6 x +3= 0. Real, equal, √(3/2)
10) 2x² +5√3 x +6 = 0. -2√3, -√3/2
11) √3x² +10x -8√3= 0. -4√3,2/√3
12) 3x² +2√5 x -5 = 0. √5/3, -√5
13) 3a²x²+ 8abx + 4b²=0, a≠0. -2b/a, -2b/3a
EXERCISE - V
** Find the values of k for which the given equation has real and equal roots:
1) x² + k(4x + k-1)+2= 0. 2/3, -1
2) x² -2x(3k+1)+7(3+2k)= 0. 2,-10/9
3) (k+1)x² -2(k -1)x + 1= 0. 0,3
4) (k -12)x² +2(k-12)x +2= 0. 12,14
5) kx² -5x + k= 0. ±5/2
6) 2x² -10x + k= 0. 25/2
7) 2x² +3x + k= 0. 9/8
8) 2x² -kx + k= 0. ±2√2
9) 9x² +3kx + 4= 0. ±4
10) 12x² +4kx + 3= 0. ±3
Mg. A- R.1
1) a/(ax -1) + b/(bx -1)= a+ b.
2) a(x² +4)= x(a²+ 4).
3) (x+3)/(x+2) = (3x - 7)/(2x - 3)
4) 2x/(x -4) + (2x - 5)/(x - 3) = 25/3
5) (x+3)/(x -2) - (1- x)/x = 17/4.
6) x/(x +1) + (x +1)/x = 34/15. (x≠ 0, x≠ -1)
7) 1/(p+q +x) = 1/p + 1/q + 1/x.
Mg. A- R.2
1) 2/(x +1) - 4/(2x - 7) = 3/(2- x).
2) (x -1)/x + x /(x - 1) = 61/30.
3) Show that 2 as well as 3 is a zero of the polynomial x²-5x+6.
4) Show that P(x)= x +9 has no real zeros.
5) x²+ 3x - 18=0. 3, -6
6) x² - 3x -10=0. 5, -2
7) 6x² - x - 2= 0. 2/3,-1/2
8) 9x²- 3x-2=0. 2/3, -1/3
Mg. A- R.3
1) (x-8)(x+4)=0. 8, -4
2) 2x²- 5x =0. 0, 5/2
3) x²-8x + 15=0. 3,5
4) 9x²+ 15x -14=0. -7/3, 2/3
5) 6x² + x - 15=0. -5/3, 3/2
6) x² -(1+√2)x +√2=0. 1, √2
7) a²x²+ (a +b)x +ab=0. - 1, -b/a
8) x² -11ax + 28a²=0. 7a,4a
Mg. A- R.4
1) 3a²x²+ 2abx - b²=0. -b/a,b/3a
2) 2x²- 3x+1=0. 1, 1/2
3) 5x² - 3x - 2=0. 1, -2/5
4) 2x²+ ax -a²=0. -a, a/2
5) 8x² - 22x - 21=0. 7/2, -3/4
6) 48x²- 13x -1=0. 1/3, -1/16
7) 3x²- 4x +1=0. 1, 1/3
8) x²- 8x +16=0. 4,4
Mg. A- R.5
1) x + 1/x= 5/2. 2, 1/2
2) a/(ax-1) + b/(bx -1) = a + b. (a+b)/ab, 2/(a+b)
3) a(x²+4)= x(a² +4). a, 4/a
4) (x+3)/(x -2) - (1-x)/x = 17/4. -2/9, 4
5) x/(x+1). +(x+1)/x = 34/15. (x≠0, x≠-1). -5/2, 3/2
6) 1/(p+q+x) = 1/p + 1/q + 1/x. -q, -p
7) 2/(x+1) - 4/(2x -7) =3/(2- x). 1/2, 5
8) (x -1)/x + x/(x -1)= 61/30. -5,6
Mg. A -R.6
1) - 3x²- 11x +4=0. 1/3, -4
2) (x²+8)/11= 5x -x² -5. 7/3, 9/4
3) 2x/(x-4) + (2x-5/(x-3)=25/3. 6, 40/13
4) (x+6)/(x+7) - (x+1)/(x+2)= 1/(3x+1). 3,3
5) √(x+2) +√(x-3)= 5. 7
6) 2√(x+5)- √(2x+8)= 2. ±4
7) √(2x+1) + √(3x+4)=7. 4, 480
8) 4x²+ 6x + √(2x²+3x+4)=13. 1, -5/2
Mg. A- R.7
1) √(2x²-x+10) - √(2x²-x+3)= 1. 2, -3/2
2) √{(x+1)/(x-1)} + √{(x-1)/(x+1)}= 5/√6. ±5
3) √{(1-x)/x} + √{x/(1-x)}= 13/6. 4/13, 9/13
4) √(x+5)+ √(x+12)= √(2x+41). -21,4
5) x² - 0.5x + 0.06= 0. 0.2, 0.3
6) x² +3x-(a -1)(a+2)= 0. (1-a),(a+2)
7) x² - (p + 1)p)x +1= 0. a, 1/a
8) x² - {a/(a+b) + (a+b)/a}x + 1= 0.
-a/(a+b), (a+b)/a
9) x² - 2ax + a² -1= 0. (a-1),(a+1)
10) x/8 + 8/x = x/2 + 2/x. 0. ±4
Mg. A-R.8
1) Find the values of k for which the equation is real roots : x²+ kx +4=0. 4
2) Determine if 3 is a root of the equation given below:
√(x² - 4x+3)+√(x²-9)=√(4x²-14x +16)
Continue............
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