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Question

If α,β,γ are the zeroes of a cubic polynomial ax3+bx2+cx+d, then the product of zeroes is

A
ba
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B
ba
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C
ca
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D
da
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Solution

The correct option is D da

Ggiven that

p(x)=ax3+bx2+cx+d .........(1) where a0 is a cubic polynomial

And α,β,γ are the zeroes of the polynomial p(x)

We can also write the polynomial in this way

p(x)=(xα)(xβ)(xγ)

p(x)=x3(α+β+γ)x2+(αβ+βγ+γα)xαβγ .............(2)

Equations (1) and (2) are same

Comparing the coefficients

a1=bαβγ=cαβ+βγ+γα=dαβγ

On solving we get the following results

α+β+γ=ba= Sum of the roots


αβ+βγ+γα=ca

αβγ=da= product of roots

Hence, option D is correct

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