Question

Pankaj's father gave him some money to buy avocado from the market at the rate of p(x) = x2 -24x + 128. Let a ,ß are the zeroes of p(x). Based on the above information, answer the following questions.
Q46. Find the value of a and B, where ac ß (a) -8,-16 (b) 8,16 (c) 8,15 (d) 4,9
Q47. Find the value ofa +B + aß (a) 151 (b) 158 (c) 152 (d) 155
Q48. The value of p(2) is (a) 80 (b) 81 (c) 83 (d) 84
Q49. If a ,Bare the zeroes of x² + x-2, then 1 B (a) (b) (c)
Q50. If the sum of zeroes of g(x) = kx² + 2x +3k is equal to their product, then k = (a) (b) (c) (d) - + ( (d) 2 3 a WIN 2 3​

Answer 1

Correct option is

A

k=0

C

k=3

The given equation is

(k+1)x

2

−2(k−1)x+1=0

comparing it with ax

2

+bx+c=0 we get

a=(k+1),b=−2(k−1) and c=1

∴ Discriminant,

D=b

2

−4ac=4(k−1)

2

−4(k+1)×1

=4(k

2

−2k+1)−4k−4

⇒4k

2

−8k+4−4k−4=4k

2

−12k

Since roots are real and equal, so

D=0⇒4k

2

−12k=0⇒4k(k−3)=0

⇒ either k=0 or k−3=0⇒4k(k−3)=0

Hence, k=0,3.