-75sqrt 5 is a root of f(x) = x^2 - 28,125. 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. ______

Identify Product of Roots: Since -75sqrt(5) is a 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 = -28,125.Let Other Root be r: Let the other root be r. Then, (-75sqrt(5)) * r = -28,125.Solve for r: Solve for r: r = -28,125 / (-75sqrt(5)).Simplify Expression: Simplify the expression: r = 375/sqrt(5).Rationalize Denominator: To rationalize the denominator, multiply the numerator and denominator by sqrt(5): r = (375sqrt(5)) / 5.Final Simplification: Simplify the fraction: r = 75sqrt(5).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$-75\sqrt{5}$ is a root of $f(x) = x^2 - 28,125$ . 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.

View step-by-step help

Home

Math Problems

Precalculus

Conjugate root theorems

Full solution

-75\sqrt{5}

is a root of

f(x) = x^2 - 28,125

. 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.

Identify Product of Roots: Since $-75\sqrt{5}$ is a 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 $c = -28,125$ .
Let Other Root be $r$ : Let the other root be $r$ . Then, $(-75\sqrt{5}) \times r = -28,125$ .
Solve for r: Solve for r: $r = \frac{-28,125}{-75\sqrt{5}}$ .
Simplify Expression: Simplify the expression: $r = \frac{375}{\sqrt{5}}$ .
Rationalize Denominator: To rationalize the denominator, multiply the numerator and denominator by $\sqrt{5}$ : $r = \frac{375\sqrt{5}}{5}$ .
Final Simplification: Simplify the fraction: $r = 75\sqrt{5}$ .