BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 83E

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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