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Chapter 6: Q 284 (page 627)

In the following exercises, solve:

4b2+7b=鈭�3

Short Answer

Expert verified

The solutions areb=-34,-1.

Step by step solution

01

Step 1. Given Information 

The given quadratic equation is4b2+7b=鈭�3.

We have to solve the quadratic equation by factoring.

02

Step 2. Factor the quadratic expression 

First, write the given equation in standard form.

The standard form of the quadratic equation is

ax2+bx+c=0

Therefore,

4b2+7b=鈭�34b2+7b+3=0

Now, let's factor the quadratic expression

4b2+7b+3=04b2+4b+3b+3=04b(b+1)+3(b+1)=0(4b+3)(b+1)=0

03

Step 3. Use the Zero Product Property

The equations we get are

4b+3=0b+1=0

Thus,

4b+3=0b=-34orb+1=0b=-1

04

Step 4. Verify the answers

To verify the answer we will substitute the solutions separately into the original equation.

Put b=-34in the given equation,

4(-34)2+7(-34)=-394-214=-3-3=-3

It is true.

Now, put b=-1in the given equation

4(-1)2+7(-1)=-34-7=-3-3=-3

It is also true.

Hence, the solutions areb=-34,-1.

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