Question

if p, q are zeroes of polynomial p(x)=7x^2-8x+k, such that p-q=2, then find value of k.​

Answer 1

Given polynomial is

f(x) = 7x² - 8x + k

Since p and q are zeroes of f(x), we have

p + q = 8/7

pq = k/7

Given, p - q = 2

Then, (p - q)² = 2²

or, (p + q)² - 4pq = 4

or, (8/7)² - 4 (k/7) = 4

or, 64/49 - 4k/7 = 4

or, 4k/7 = 64/49 - 4

or, 4k/7 = (64 - 196)/49

or, 4k/7 = - 132/49

or, k = - 132/49 * 7/4

or, k = - 33/7

The value of k is (- 33/7).