Question

α and β are zeroes of the polynomial x2 + 8x +12, find the values of (a) α2 + β 2 (b) 3 + 3 (c) 3 + 3 .​

Answer 1

Step-by-step explanation:

Given α and β be the zeroes of polynomials, so the quadratic polynomial is x

2

−(α+β)x+αβ , comparing the above equation to the given equation, x

2

−2x−8, so we have,

α+β=2 and αβ=−8

So, 3α+3β=3(α+β)=3×2=6 and 3α×3β=9αβ=9×(−8)=−72

Thus, the required quadratic polynomial is x

2

−3(α+β)x+9αβ

Putting the values of α+β and αβ in above equation, x

2

−6x−72