-98sqrt 3 is a root of f(x) = x^2 - 28,812. Find the other roots of f(x). Write your answer as a list of simplified values separated by commas, if there is more than one value. ______

Given root information: Since -98√3 is a root, the other root must also be -98√3 because the coefficients of the polynomial are real numbers, and non-real roots of polynomials with real coefficients always come in conjugate pairs.Using product of roots: To find the other root, we can use the fact that the product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a. Here, a = 1 and c = -28,812.Calculate product: The product of the roots is (-98√3) * (other root) = -28,812.Find other root: Divide -28,812 by -98√3 to find the other root: (other root) = -28,812 / (-98√3).Simplify expression: Simplify the expression: (other root) = 294√3.

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Precalculus

Conjugate root theorems

Full solution

-98\sqrt{3}

is a root of

f(x) = x^2 - 28,812

. Find the other roots of

f(x)

\newline

Write your answer as a list of simplified values separated by commas, if there is more than one value.

\newline

______

\newline

Given root information: Since $-98\sqrt{3}$ is a root, the other root must also be $-98\sqrt{3}$ because the coefficients of the polynomial are real numbers, and non-real roots of polynomials with real coefficients always come in conjugate pairs.
Using product of roots: To find the other root, we can use the fact that the product of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{c}{a}$ . Here, $a = 1$ and $c = -28,812$ .
Calculate product: The product of the roots is $(-98\sqrt{3}) \times (\text{other root}) = -28,812.$
Find other root: Divide $-28,812$ by $-98\sqrt{3}$ to find the other root: $(\text{other root}) = \frac{-28,812}{-98\sqrt{3}}$ .
Simplify expression: Simplify the expression: $(\text{other root}) = 294\sqrt{3}$ .