Question

Find the solutions to the equation below check all that apply

4x^2-8x+3=0

A. x=3/2
B. x=2
C. x=3
D. x=1/2
E. x=-1/2
F. x=-2

Answer 1

Hence, the correct options are A and D.

Explanation:

`4x^2-8x+3=0`

Splitting the term (-8x) by using middle term splitting theorem:

`4x^2-2x-6x+3=0`

`2x(2x-1)-3(2x-1)=0`

`(2x-1)(2x-3)=0`

`2x-1=0`

`x=(1)/(2)`

`(2x-3)=0`

`x=(3)/(2)`

The solution of the given equation
`4x^2-8x+3=0` :

`x=(1)/(2),(3)/(2)`

Hence, the correct options are A and D.

Answer 2

A. x=3/2

D. x=1/2

Solve for x over the real numbers:

4 x^2 - 8 x + 3 = 0

The left hand side factors into a product with two terms:

(2 x - 3) (2 x - 1) = 0

Split into two equations:

2 x - 3 = 0 or 2 x - 1 = 0

Add 3 to both sides:

2 x = 3 or 2 x - 1 = 0

Divide both sides by 2:

x = 3/2 or 2 x - 1 = 0

Add 1 to both sides:

x = 3/2 or 2 x = 1

Divide both sides by 2:

Answer: x = 3/2 or x = 1/2