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Chapter 9: Q. 159 (page 906)

In the following exercises, solve. 2x4-5x2+3=0

Short Answer

Expert verified

Solution for equation will be

  • x=+32
  • x=-32
  • x=+1
  • x=(-1)

Step by step solution

01

Step 1.  Given Data

Quadratic Equation is2x4-5x2+3=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 -

2x4-5x2+3=0

2(x2)2-5x2+3=0

Put the value of x2=u

2u2-5u+3=0

(u-32)(u-1)=0

By using Zero product property -

u-32=0, u-1=0

u=32, u=1

04

Step 4.  Calculation

Replace u with x2

x2=32, x2=1

Using the square root property -

x=卤32, x=卤1

x=卤32, x=卤1

There are four solutions -

  • x=+32
  • x=-32
  • x=+1
  • x=-1

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