Question

If α and β are zeroes of polynomial 3x2 +2x – 6, then find the value of :- α2 + β2 please answer the question. ​

Answer 1

here , given polynomial is 3x²+2x-6

on comparing with ax²+bx+c

we get, a=3, b=2 and c= -6

α+β= -b/a = -2/3

αβ=c/a=-6/3= -2

Now, α²+β²= (α+β)²-2αβ

=(-2/3)²-2× -2

=4/9+4=40/9.

Answer 2

From the question, if α and β are zeros of polynomial ρ(x), then
α + β = 2
αβ = (3)x(-6) = -18

α^2 + β^2 = (α + β)^2 -2αβ
= 2^2 - (2)x(-18)
= 4 + 36
= 40