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Chapter 6: Q. 308 (page 627)

Solve quadratic equations by factoring.

m3-2m2=-m

Short Answer

Expert verified

The roots are0and1.

Step by step solution

01

Step 1. Rearrange the terms

Rearranging the terms to bring them on a single side,

m3-2m2+m=0

02

Step 2. Factor the greatest common factor

Factoring out the greatest common factor first,

m(m2-2m+1)=0

03

Step 3. Simplify the quadratic equation

We factor the trinomial first,

m(m2-2m+1)=0m(m-1)(m-1)=0

Use the Zero Product Property to set each factor to 0, we get,

m=0,m=1, m=1

04

Step 4. Check

Resubstitute each of the roots separately into the original equation.

When m=0,

m3-2m2=-m0-0=00=0

When m=1,

m3-2m2=-m13-2(1)2=-11-2=-1-1=-1

Thus, both roots satisfy the original equation.

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