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Question

If the zeroes of the polynomial x33x2+x+1 are m – n, m and m + n, find m and n.

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Solution

We know that for the cubic polynomials, sum of the zeroes = ba

m – n + m + m + n = 3 3m = 3 m = 1

Sum of the product of the zeroes (taken 2 at a time) =ca

(mn)×m+m×(m+n)+(m+n)×(mn)=13m2n2=1n2=2n=±2


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