Question

Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.

X= - 2, x = 10

Answer 1

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Explanation:

To write a polynomial function of least degree with rational coefficients that has the given roots, we can use the factor theorem. The factor theorem states that if r is a root of a polynomial function P(x), then x - r is a factor of P(x).

In this case, the roots of the polynomial are x = -2 and x = 10. We can use the factor theorem to write a polynomial function that has these roots as follows:

P(x) = (x + 2)(x - 10)

This polynomial function has degree 2, which is the least degree possible, and all of its coefficients are rational numbers. It has roots x = -2 and x = 10, as required.