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Chapter 6: Q 285 (page 627)

In the following exercises, solve:

4m2=17m鈭�15

Short Answer

Expert verified

The solution ism=3.

Step by step solution

01

Step 1. Given Information

The given quadratic equation is4m2=17m鈭�15.

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,

4m2=17m鈭�154m2-17m+15=0

Now, let's factor the quadratic expression

4m2-17m+15=04m2-12m-5m+15=04m(m-3)-5(m-3)=0(4m-5)(m-3)=0

03

Step 3. Use the Zero Product Property 

The equations we get are

4m-5=0m-3=0

Thus,

4m-5=0m=54orm-3=0m=3

04

Step 4. Verify the answers 

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

Put m=54in the given equation,

4(54)2=17(54)-1554=854-1554-854=-15-20=-15

It is false.

Now, put m=3in the given equation

4(3)2=17(3)-1536=51-1536=36

It is true.

Hence the solution ism=3.

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