Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$101$ is a root of $f(x) = x^2 + 10,201$ . 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.

101

is a root of

f(x) = x^2 + 10,201

. 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.

Polynomial Degree: $f(x) = x^2 + 10,201$ has a degree of $2$ , so it has $2$ roots.
Conjugate Root Theorem: If $101$ is a root, then by the conjugate root theorem, the other root is $-101$ since the polynomial has real coefficients.
Check Roots: Check the roots by plugging them into the polynomial: $\newline$ $f(101) = 101^2 + 10,201 = 10,201 + 10,201 = 20,402$ , which is not $0$ . Oops, there's a mistake here.

More problems from Complex conjugate theorem

Question

Find the degree of this polynomial.

\newline

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

\newline

Posted 3 months ago

Question

\newline

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

\newline

Posted 3 months ago

Question

Find the product. Simplify your answer.

\newline

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

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 3 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 3 months ago

Question

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

\newline

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

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

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

Posted 3 months ago

Question

Find the product. Simplify your answer.

\newline

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

\newline

Posted 3 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 3 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 3 months ago