Question

Find the polynomial function with roots 1, –2, and 5

Answer 1

start with the polynomial in factored form, then multiply out

Answer 2

When x = 1,-2 and 5 and f(x) = 0, then the factors are (x - 1)(x + 2)(x - 5) = 0.

(x - 1)(x + 2)(x - 5) = 0

Multiplying each term by term and combining like terms, we obtain:

(x² + x - 2)(x - 5) = 0
x³ - 5x² + x² - 5x - 2x + 10 = 0
x³ - 4x² - 7x + 10 = 0

Hence, f(x) = x³ - 4x² - 7x + 10.

I hope this helps!

Answer 3

since you know the zeros are 1, -2 and 5, you know it factors as
\[p(x)=(x-1)(x+2)(x-5)\] although you do not know the leading coefficient is 1, so you are finding A polynomial, not THE polynomial