Question

if alpha and beta are the zeros of the polynomial 2x^2+4x+2 find the value of alpha / beta + beta / alpha - 4 alpha beta

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Answer 1

Answer:

(α+β)2=α2+β2+2αβ⇒α2+β2=(α+β)2−2αβ

Theorem : If ax2+bx+c has 2 different zeroes α and β then :

α+β=−ba and αβ=ca

If we apply that to our problem, we have : α+β=42=2 and αβ=−32

Thus α2+β2=(α+β)2−2αβ=(2)2–2×−32=7