Question

Apply the Fundamental Theorem of Algebra to determine how many imaginary roots g(x)=12x−3x2+13x3−9 will have, if you know it has one x-intercept.(1 point) Responses one imaginary root one imaginary root two imaginary roots two imaginary roots three imaginary roots three imaginary roots no imaginary roots

Answer 1

The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n complex roots, including both real and imaginary roots.

In this case, we know that the polynomial g(x) has one x-intercept, which means it has one real root. Since g(x) is a polynomial of degree 3 (the highest power of x is 3), the Fundamental Theorem of Algebra tells us that g(x) has a total of 3 complex roots.

Therefore, g(x) will have two imaginary roots.