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Chapter 9: Q. 155 (page 906)

In the following exercises, solve. x4-7x2+12=0

Short Answer

Expert verified

Solution for equation will be

  • x=+2
  • x=-2
  • x=+3
  • x=-3

Step by step solution

01

Step 1.  Given Data

Quadratic Equation is x4-7x2+12=0

02

Step 2.  To Find

We have to solve it and find the value of x.

03

Step 3.  Explanation

Let the value of x2=u

Then the equation is -

x4-7x2+12=0

(x2)2-7x2+12=0

Put the value of x2=u

u2-7u+12=0

(u-4)(u-3)=0

By using Zero product property -

u-4=0, u-3=0

u=4, u=3

04

Step 4.  Calculation

Replace u with x2

x2=4, x2=3

Using the square root property -

x=卤4, x=卤3

x=卤2, x=卤3

There are four solutions -

  • x=+2
  • x=-2
  • x=+3
  • x=-3

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