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Chapter 6: Q. 311 (page 627)

Solve quadratic equations by factoring.

36x3+24x2=-4x

Short Answer

Expert verified

The roots are0,-13.

Step by step solution

01

Step 1. Rearrange the terms

Rearranging the terms to bring them on a single side,

36x3+24x2+4x=0

02

Step 2. Factor the greatest common factor

Factoring out the greatest common factor first,

4x(9x2+6x+1)=0

03

Step 3. Simplify the quadratic equation

We factor the trinomial first,

4x(9x2+6x+1)=04x(9x2+3x+3x+1)=04x(3x(3x+1)+1(3x+1))=04x(3x+1)(3x+1)=04x(3x+1)2=0

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

when 4x=0,

x=0

when 3x+1=0,

x=-13

04

Step 4. Check

Resubstitute each of the roots separately into the original equation.

When x=0,

36x3+24x2=-4x36(0)3+24(0)2=-4(0)0+0=00=0

This is true.

When x=-13,

36x3+24x2=-4x36((-13)3)+24((-13)2)=-4(-13)36(-127)+24(19)=43-43+83=4343=43

This is also true.

Thus, both roots satisfy the original equation.

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Most popular questions from this chapter

In the following exercises, factor completely using the perfect square trinomials pattern.

36s2+84s+49

In the following exercises, factor the greatest common factor from each polynomial.

3x2+6x-9

In the following exercises, factor the greatest common factor from each polynomial.

8p2+4p+2

Factor using the 鈥榓c鈥� method:

6x2+13x+2.

Factor Trinomials of the Form ax2+bx+cUsing Trial and Error.

2t2+7t+5
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