Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Solve the equation x^(3)+2x^(2)-5x-6=0 given that 2 is a zero of f(x)=x^(3)+2x^(2)-5x-6 The solution set is {:'. (Use a comma to separate answers as needed.)$

Solve the equation $x^{3}+2 x^{2}-5 x-6=0$ given that $2$ is a zero of $f(x)=x^{3}+2 x^{2}-5 x-6$ $\newline$ The solution set is $\{\because$ . (Use a comma to separate answers as needed.)

View step-by-step help

View step-by-step help

Complex conjugate theorem

Full solution

Q. Solve the equation

x^{3}+2 x^{2}-5 x-6=0

given that

2

is a zero of

f(x)=x^{3}+2 x^{2}-5 x-6

\newline

The solution set is

\{\because

. (Use a comma to separate answers as needed.)

Divide by x - $2$ : Use synthetic division or polynomial long division to divide the polynomial by $x - 2$ since $2$ is a zero of $f(x)$ .
Perform synthetic division: Perform the synthetic division with $2$ as the zero. $\newline$ $\begin{array}{r|rrrr} 2 & 1 & 2 & -5 & -6 \\ & & 2 & 8 & 6 \\ \hline & 1 & 4 & 3 & 0 \\ \end{array}$ $\newline$ The resulting polynomial after division is $x^2 + 4x + 3$ .
Factor quadratic polynomial: Factor the quadratic polynomial $x^2 + 4x + 3$ . $\newline$ $x^2 + 4x + 3 = (x + 1)(x + 3)$
Find other roots: Set each factor equal to zero to find the other roots. $\newline$ $x + 1 = 0 \quad \text{and} \quad x + 3 = 0$ $\newline$ Solving these equations gives us the roots $x = -1$ and $x = -3$ .

More problems from Complex conjugate theorem

Question

Find the degree of this polynomial.

\newline

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

\newline

Posted 2 months ago

Question

\newline

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

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

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

\newline

Posted 1 month ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 2 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 2 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 2 months ago

Question

Find the product. Simplify your answer.

\newline

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

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 2 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 2 months ago