Question

Find the zeroes of the polynomial f(x)= x³-5x²-16x + 80, if it is given that the product of its two zeroes is 12. please help and don't write wrong answers class 10 ppolynomials​

Answer 1

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Find the zeros of the polynomial f(x)=x3−5x2−2x+24 if it is given that the product of its two zero is 12.

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Let α,β and y be the zeros of polynomial f(x) such that ab=12

We have, α+β+y=a−b=1−(−5)=5

αβ+βy+yα=ac=1−2=−2 and  αβy=a−d=1−24=−24

Putting αβ=12 in αβy=−24, we get

12y=−24                           ⇒                                         y=−1224=−2 

Now ,α+β+y=5            ⇒            α+β−2=5

⇒ α+β=

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