Question

α, β are zeroes of the polynomial 3x² – 8x + k. Find the value of k, if `α^2 + β^2 = 40/9`.

Answer 1

3x² – 8x + k

Roots are α and β.

`α + β = (-b)/a`

= `-((-8))/3`

= `8/3`

`αβ = c/a`

= `k/3`

Now α² + β² = (α + β)² – 2αβ

= `(8/3)^2 - (2k)/3`

Given, `α^2 + β^2 = 40/9`

`40/9 = 64/9 - (2k)/3`

`40/9 - 64/9 = (-2k)/3`

`(-24)/9 = - (-2k)/3`

k = `(24 xx 3)/(2 xx 9)`

k = 4