Question

if alpha and beta are the zeros of the polynomial x^2+3x-2, then the value of 1/alpha^2 + 1/beta^2 is
pls help​

Answer 1

Explanation:

Given that α & β are zero of polynomial

f(x)=x2−3x−2

therefore α+β=3

αβ=−2

Now, the zero of the required quadratic polynomial are,

2α+β1 & 2β+α1

Sum of the roots-

2α+β1+2β+α1=(2α+β)(2β+α)2β+α+2α+β=4αβ+2α2+2β2+αβ3(α+β)

=4×(−2)+2[(α+β)2−2αβ]+(−2)3×3

=−10+2[9+2×2]9

=−10+269

=169

Products of roots:-

2α+β1×2β+α1=