Question

If α and β are two zeros of the polynomial 2x²+7x+5 then α²/β+β²/α=​

Answer 1

Answer:

Given the roots of the equation:

2x²+7x+5=0 are α,β

Compare it with:

ax²+bx+c=0

So:

a=2

b=7

and c=5

We know that:

α+β=-b/a

=-7/2...............(1)

α*β=c/a

=5/2.............(2)

Given,

α²/β+β²/α

=α³+β³/α*β

=(α+β)(α²-αβ+β²)/αβ

=(α+β)[(α+β)²-αβ]/αβ

From (1) and (2)

=(-7/2)[(-7/2)²-5/2]/5/2

=[(-7/2)(49/4-5/2)]/5/2

=[(-7/2)(49-10)/4]/5/2

=-7/2*39/4*2/5

=-273/20

=-27.3/2

=-13.65

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