Question

If one zero of the polynomial x² − 8x + k exceeds the other by 2, then find the zeroes and value of k.

Answer 1

Given polynomial is x² − 8x + k.

On comparing with ax² + bx + c, we get

a = 1, b = −8 and c = k

Let one of the zeroes be α.

∴ Other zero is α + 2.

We know that

Sum of zeroes = `-b/a`

∴ α + α + 2 = `-b/a`

∴ 2α + 2 = `-((-8))/1`

∴ 2(α + 1) = 8

∴ α + 1 = 4

∴ α = 3

Therefore, one zero is 3 and other is 3 + 2 = 5 Now, we find the value of k.

∵ Product of zeroes = `c/a`

∴ α x (α + 2) = `k/1`

∴ 3 × 5 = `k/1`

∴ k = 15

Hence, the value of k is 15.