Question

If α and β are the zeroes of the polynomial f(x) = x² – 4x – 5 then find the value of α² + β².

Answer 1

Given, polynomial f(x) = x² – 4x – 5

On comparing it by ax² + bx + c, we get

a = 1, b = – 4 and c = – 5

Since, given α and β are the zeroes of the polynomial.

∴ Sum of zeroes,

`α + β = - b/a`

= `(-(-4))/1`

= 4

And product of zeroes,

`αβ = c/a`

= `(-5)/1`

= –5

Now, α² + β² = (α + β)² – 2αβ

= (4)² – 2(–5)

= 16 + 10

= 26