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in Polynomials by (32.2k points)
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Find a cubic polynomial whose zeroes are 3, 5 and -2.

1 Answer

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Best answer

Let α, β and γ are the zeroes of the required polynomial. 

Then we have: 

α + β + γ = 3 + 5 + (-2) = 6 

αβ + βγ + γα = 3 × 5 + 5 × (-2) + (-2) × 3 = -1 

and αβγ = 3 × 5 × -2 = -30 

Now, p(x) = x3 – x2 (α + β + γ) + x (αβ + βγ + γα) – αβγ 

= x3 – x2 × 6 + x × (-1) – (-30) 

= x3 – 6x2 – x + 30 

So, 

the required polynomial is p(x) = x3 – 6x2 – x + 30.

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