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Find a cubic polynomial whose zeros are 3, 5 and ‒2.
Let us assume be the zeros of the required polynomial
We have,
= 3 + 5 + (- 2) = 6
= 3 × 5 + 5 × (- 2) + (- 2) × 3 = - 1
And, = 3 × 5 × - 2 = - 30
Now, we have:
p (x) = x3 – x2 () + x (
) –
= x3 – x2 × 6 + x × (- 1) – (- 30)
= x3 – 6x2 – x + 30
Hence, the required polynomial is p (x) = x3 – 6x2 – x + 30