polyomial

Let α and β be the roots of the polynomial f(x)=x² -8x+k

Then,  α + β = 8     and  αβ = k

According to the question, α²+ β² = 40

α²+ β²  = (α+ β)² - 2αβ

On sunstitution, we get

40 = 8² - 2k

40 = 64 - 2k

2k = 24

k =12