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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 3x3−12x2+3x+18A cubic polynomial having zeroes α, β and γ can be written as: k[x3−(α+β+γ)x2+(αβ+βγ+αγ)x−αβγ] ...(i) We have, α + β + γ = 4 αβ + βγ + γα = 1 αβγ = – 6 Substituting these values in (i), we get k[x3−4x2+x+6] For x = 3, the polynomial becomes 3×[x3−4x2+x+6]=3x3−12x2+3x+18 Hence, the correct answer is option (c).

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