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Question

A cubic polynomial whose zeroes are α, β and γ such that α + β + γ = 4, αβ + βγ + γα = 1 and αβγ = – 6 can be

A
2x38x2+x+12
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B
3x312x2+3x+18
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C
4x316x24x24
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D
x3+4x2x6
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Solution

The correct option is B 3x312x2+3x+18
A cubic polynomial having zeroes α, β and γ can be written as:

k[x3(α+β+γ)x2+(αβ+βγ+αγ)xαβγ] ...(i)

We have,

α + β + γ = 4

αβ + βγ + γα = 1

αβγ = – 6

Substituting these values in (i), we get

k[x34x2+x+6]

For x = 3, the polynomial becomes

3×[x34x2+x+6]=3x312x2+3x+18

Hence, the correct answer is option (c).

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