Question

Write a polynomial function of least degree with rational coefficients so that ​P(x)0 has the given roots. x=-5, x=10

Answer 1

P(x) = x² - 15x + 50

Explanation:

We write the polynomial function P(x), given that P(x) = 0 has the given roots, x = 5 and x = 10.

Since x = 5 and x = 10 are the roots of P(x) = 0, it follows that (x - 5) and (x - 10) are factors of P(x) = 0. So, P(x) = (x -5)(x - 10) = 0

Expanding the brackets, we have

x² - 10x - 5x + 50 = 0

Simplifying, we have

x² - 15x + 50 = 0 = P(x)

Thus,

P(x) = x² - 15x + 50