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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 cubic polynomial whose zeroes are α, β and γ such that α + β + γ = 4, αβ + βγ + γα = 1 and αβγ = – 6 can be
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Solution
The correct option is B 3x3−12x2+3x+18
A 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).
A 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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