Question

if a b are the zeros of the polynomial ax²+ bx+c , then find the value of 1/a²+1/b²​

Answer 1

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Step-by-step explanation:

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Answer 2

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Answer :

Given :α and β are two zeros of the polynomial

Equation f ( x ) = ax2 + bx + c

So,

We know from relationship between zeros and coefficient ,

Sum of zeros = −coefficient xcoefficient of x2 , So

α + β = - ba --- ( 1 )

And

Product of zeros = constant termcoefficient of x2 , So

αβ = ca ------ ( 2 )

We find value of 1α2 + 1β2 , As:

⇒α2 +β2 α2β2 ⇒(α +β )2 − 2αβ α2β2 [We know (a + b)2 = a2 + b2 + 2ab] Now , Substitute values from equation (1) and (2) , we get ⇒(−ba)2 − 2(ca)(ca)2⇒(b2a2) − 2(ca) (ca)2⇒[b2 − 2aca2 ]c2a2⇒b2 − 2aca2×a2c2⇒[b2 − 2acc2 ]