Question

If the sum of squares of the zeroes of the quadratic polynomial x² – 8x + k is 40, find k.

Answer 1

Given : p(x) = x² – 8x + k

α² + β² = 40

We have,

Now, if we recall the identities

(a + b)² = a² + b² + 2ab

Using the identity, we get

(α + β)² = α² + β² + 2 αβ

(8)² = 40 + 2(k)

⇒2k = 64 – 40

k = 24/2 = 12