Question

Find the remaining roots of the following polynomial. One of the factors is (x + 2).

f(x) = 84 - 9.13 - 23x^2 + 9x + 22.
a) -4, 11, -1, 1
b) 11, -1.1
c) -13, -1, 1
d) -10, -1.1

Answer 1

To find the remaining roots of the polynomial, rearrange it into a quadratic equation. Use the quadratic formula to solve for the remaining roots. The correct answer is option c) -13, -1, 1.

Step-by-step explanation:

To find the remaining roots of the polynomial, we begin by rearranging the polynomial into a quadratic equation equal to 0. The given factor (x + 2) implies that (x = -2) is one of the solutions. Using long division, we can divide the polynomial by (x + 2) to obtain a quadratic equation.

Next, we can solve the quadratic equation by applying the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a). Substituting the values of a, b, and c from the quadratic equation, we can plug in the values and calculate the remaining roots of the polynomial.

In this case, the remaining roots are -1 and 1, therefore, the correct answer is option c) -13, -1, 1.