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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) = x^{3} – x^{2} () + x () –

= x^{3} – x^{2} × 6 + x × (- 1) – (- 30)

= x^{3} – 6x^{2} – x + 30

Hence, the required polynomial is p (x) = x^{3} – 6x^{2} – x + 30

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