Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$119$ is a root of $f(x) = x^2 + 14,161$ . 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

View step-by-step help

Complex conjugate theorem

Full solution

Q.

119

is a root of

f(x) = x^2 + 14,161

. 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.

Write as $x - 119$ : Since $119$ is a root, we can write it as $x - 119 = 0$ . Now we need to find the other root by factoring the polynomial. $\newline$ $f(x) = x^2 + 14,161$ can be rewritten as $f(x) = (x - 119)(x - a)$ where $a$ is the other root we need to find.
Find other root: To find the value of $a$ , we expand the factored form and compare coefficients. $(x - 119)(x - a) = x^2 - (119 + a)x + 119a$ The constant term in the polynomial $f(x)$ is $14,161$ , so we set $119a$ equal to $14,161$ .
Expand and compare coefficients: Solving for 'a', we divide $14,161$ by $119$ . $\newline$ $a = \frac{14,161}{119}$ $\newline$ $a = 119$

More problems from Complex conjugate theorem

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 5 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 5 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 5 months ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 5 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 5 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 5 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 9 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 9 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 9 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant