-79sqrt 3 is a root of f(x) = x^2 - 18,723. 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. ______

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-79sqrt 3 is a root of f(x) = x^2 - 18,723. 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. ______

Bytelearn · Accepted Answer

Given root information: Since -79√3 is a root, the other root must also be -79√3 because the coefficients of the polynomial are real numbers, and non-real roots of polynomials with real coefficients always come in conjugate pairs.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 = -18,723.Calculate other root: The product of the roots is (-79√3) * (other root) = -18,723.Simplify expression: Divide both sides by -79√3 to find the other root: (other root) = -18,723 / (-79√3).Rationalize denominator: Simplify the expression: (other root) = 18,723 / (79√3).Calculate final answer: Rationalize the denominator by multiplying the numerator and denominator by √3: (other root) = (18,723√3) / (79 * 3).Calculate the simplified value: (other root) = (18,723√3) / 237.Divide 18,723 by 237 to get the final answer: (other root) = 79√3.

$-79\sqrt{3}$ is a root of $f(x) = x^2 - 18,723$ . 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.

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−793-79\sqrt{3}−793​ is a root of f(x)=x2−18,723f(x) = x^2 - 18,723f(x)=x2−18,723. Find the other roots of f(x)f(x)f(x).\newlineWrite your answer as a list of simplified values separated by commas, if there is more than one value.

$-79\sqrt{3}$ is a root of $f(x) = x^2 - 18,723$ . 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.