# The real solutions of the equation x 4 − x 2 − 9 = 0 .

### 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, Problem 78RE
To determine

## To calculate: The real solutions of the equation x4−x2−9=0 .

Expert Solution

The solutions of the equation are x=1.594 and x=1.594 .

### Explanation of Solution

Given information:

The equation is given as x4x29=0 .

Formula used:

In order to find all the solutions to higher-degree equation, use synthetic division, factoring, and the Quadratic Formula.

In order to Factorise the high degree polynomial, determine all the terms that were multiplied together to get the given polynomial. Then try to factor each of the terms found in the first step. This continues until it can’t be factored anymore. When it can’t be factored, then polynomial is completely factored.

For an equation of the form ax2+bx+c=0 , the solution is given by quadratic formula given by:

x=b±b24ac2a .

Calculation:

Consider the equation x4x29=0 .

Convert this equation into quadratic equation by taking x2=w .

Then, the equation x4x29=0 can be written as w2w9=0 .

Therefore, the solution of this equation is given by w=(1)±(1)24(1)(9)2(1)=1±1+362=1±372=2.54 .

Now , since x2=w . Hence, x=±2.54

Thus, the real solutions of x4x29=0 are x=1.594 and x=1.594 .

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