Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. Write the function in standard form. -2, 1+square root of 7

Question

Write a polynomial function f of least degree that has

Answer 1

zeros: -2, 1+sqr7, 1-sqr7

irrational zeros come in conjugate pairs

if 1+sqr7 is a zero, then so is 1-sqr7

x=-2

x+2 is a factor

x=1+sqr7

x-1 = sqr7

(x-1)^2 = 7

x^2 -2x +2 = 7

x^2-2x +2-7 =0

x^2 -2x -5 = 0

x^2-2x-5 is another factor

multiply the two factors together

f(x) = (x^2-2x-5)(x+2)

f(x) = x^3 -9x +10 is the polynomial with least degree and the given zeros