Question

Form a cubic polynomial whose zeros are 3, 5 and -2

Answer 1

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the required polynomial is↓
${x}^{3} - 6 {x}^{2} - x + 30$
★ for further details refer to the attachment
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Answer 2

Answer:

$\text{The cubic polynomial is }x^3-6x^2-x+30$

Step-by-step explanation:

Given the zeroes of polynomial 3, 5 and -2

we have to find the cubic polynomial.

As 3, 5 and -2 are zeroes

⇒ (x-3)(x-5)(x+2) are the factors of cubic polynomial

To find the cubic polynomial in standard form we have to simplify the above expression

$(x-3)(x-5)(x+2)\\\\=(x(x-5)-3(x-5))(x+2)\\\\=(x^2-5x-3x+15)(x+2)\\\\=(x^2-8x+15)(x+2)\\\\=x(x^2-8x+15)+2(x^2-8x+15)\\\\=x^3-8x^2+15x+2x^2-16x+30\\\\=x^3-6x^2-x+30$

which is required polynomial.