# The number of real solutions with the help of discriminant. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.5, Problem 83E
To determine

## The number of real solutions with the help of discriminant.

Expert Solution

There will be no real roots for the equation.

### Explanation of Solution

Given information:

4x2+5x+138=0

Formula used: -

When  b24ac=0  there is one real root.

When  b24ac>0  there are two real roots.

When  b24ac<0  there are two complex roots.

4x2+5x+138=032x2+40x+13=0

Now, finding discriminant to find number of real solutions:

a=32,b=40,c=13

b24ac=(40)24(32)(13)b24ac=16001664b24ac=64

Square root of a negative number is always an imaginary number:

b24ac<0

Hence, there be no real roots for equation 4x2+5x+138=0 .

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