Question

17. If a and B are zeroes of the polynomial f (x) = x^-x
- k, such that a - B = 9, find k.
A Roard Term-1, 2013, Set FFC]​

Answer 1

p(x) = x² - x - k

Given:

• Difference of Zeroes = A - B = 9 ...(1)

We know, In a quadratic polynomial:

Sum of Zeroes = -(coefficient of x) ÷ coefficient of x²

•°• A + B = -(-1) ÷ 1

A + B = 1 ...(2)

Adding (1) and (2)

A + B + A - B = 9 + 1

A + A = 10

2A = 10

A = 5

PUTTING VALUE OF X IN (2)

A + B = 1

5 + B = 1

B = - 4

On putting one of its zeroes in p(x) , it equals to zero.

•°• p(5) = 0

=> (5)² - 5 - k = 0

=> 25 - 5 - k = 0

=> 20 - k = 0

=> k = 20

Answer: K = 20