IXL - Solve equations using a quadratic pattern (Precalculus practice)

Solve.

–

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

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Learn with an example

question

Solve.

–

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

key idea

An expression in quadratic form can be written as

where

and

are numbers with

≠

and

is some expression in

Factor

Theorem:

The binomial

–

is a linear factor of the polynomial

(

)

if and only if

is a zero (or root) of

(

)

solution

Try writing the polynomial

–

in quadratic form by substituting

for an expression in

A good choice is

Then, factor the quadratic in

to find its roots.

–

(

)

–

Substitute

(

–

)

Factor

Now, by the Factor Theorem,

Substitute

to find the corresponding values of

Substitute

So, the equation has 2 solutions:

and

–

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

E.7Factor using a quadratic pattern

D.5Solve a quadratic equation using square roots

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