Question

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Answer 1

The cubic polynomial is: x³ - x² - 6x.

Explanation:

Given the degree and the roots of the polynomial we can find it.

An n - degree polynomial has n roots.

Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.

Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.

(x + 2)(x - 0)(x - 3) = 0

Multiplying them we get:

⇒
`$ (x^2 + 2x)(x - 3) $`

`$ = x^3 - 3x^2 + 2x^2 - 6x $`

`$ = x^3 - x^2 - 6x $` which is the required cubic polynomial.

Hence, the answer.