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Chapter 11: Q. 310 (page 1069)

Solve quadratic equations by factoring.

3y3+48y=24y2

Short Answer

Expert verified

The roots are0,4.

Step by step solution

01

Step 1. Rearrange the terms 

Rearranging the terms to bring them on a single side,

3y3-24y2+48y=0

02

Step 2. Factor the greatest common factor

Factoring out the greatest common factor first,

3y(y2-8y+16)=0

03

Step 3. Simplify the quadratic equation

We factor the trinomial first,

3y(y2-8y+16)=03y(y2-4y-4y+16)=03y(y(y-4)-4(y-4))=03y(y-4)(y-4)=0

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

when 3y=0,

y=0

when y-4=0

y=4

04

Step 4. Check

Resubstitute each of the roots separately into the original equation.

When y=0,

3y3+48y=24y23(0)3+48(0)=24(0)0=0

This is true.

When y=4,

localid="1661950054589" 3y3+48y=24y23(4)3+48(4)=24(4)2192+192=384384=384

This is also true.

Thus, both roots satisfy the original equation.

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