# The domain of the expression 4 x 2 − 10 x + 3 . ### 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 1.4, Problem 5E
To determine

## The domain of the expression 4x2−10x+3 .

Expert Solution

The domain of the given expression is R

Where R is real number

### Explanation of Solution

Given information:

The given expression is provided below

4x210x+3

Formula used:

Use the expression to convert into the complete square form .

That is (a±b)2=a2±2ab+b2

Calculation:

Consider the expression as,

4x210x+3=0

On Divide both side by 4 ,we have

x2104x+34=0

Now convert into the whole square form

x2104x+34=0

x 2 2. 5 4 x+ ( 5 4 ) 2 ( 5 4 ) 2 + 3 4 =0

(x 5 4 ) 2 ( 5 4 ) 2 + 3 4 =0

(x 5 4 ) 2 25 16 + 3 4 =0

(x 5 4 ) 2 25+12 16 =0

(x 5 4 ) 2 13 16 =0

(x 5 4 ) 2 = 13 16

(x 5 4 )= 13 16

x= 13 16 + 5 4

For any value of x ,the equation will satisfies.

Therefore the x(,)

So the x belongs from whole real number.

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