Question

Identify the simplest polynomial function having integer coefficients with the given zeros. 0,-4,√3.

A. P(x) = x^4 + 4x³ - 3x² -12x
B. P(x) = x^4 + 4x³ -12x² - 3x
C. P(x) = x³ + 4x² - 12x - 3
D. P(x) = x³ + 4x² - 3x - 12

Answer 1

x^4+x^3-3x^2-12x

Explanation:

0,-4,√3 are the zeros of polynomial. P.

If x=√3 is a zero and P has integer coefficients, then x=-√3 is also a zero. Both of these results come from solving the equation x^2=3 or x^2-3=0 so x^2-3 is a factor of P.

x=0 is a zero, means x-0 or x is a factor.

x=-4 is a zero, means x-(-4) or x+4 is a factor.

So the polynomial, P, in factored form is

x(x^2-3)(x+4)

Let's write in standard form.

I will begin by multiplying the last two factors.

x(x^3+x^2-3x-12)

Distribute x

x^4+x^3-3x^2-12x