What are the solution to the equation `4x ^(2) -24x+16=0` ?

Options

A. `x =3 pm sqrt5`
B. `x =4 pm sqrt6`
C. `x =5 pm sqrt3`
D. `x =5pm 2 sqrt2`

Answer

A

Explanation

The given equation is
`4x ^(2) -24x + 16 =0,` but there is a common factor of 4 in all the terms, so this becomes `x ^(2) -6x +4 =0.` Therefore, `a =1,b=-6, and c =4.`
The radicals in the answer choices are a strong clue that the quadratic formula is the way to solve this equation. The quadratic formula is `x = (-b pmsqrt(b ^(2) - 4 ac ))/(2a ),` and after you plug in the coefficients, you get:
`x = (6 pm sqrt(-6 ^(2)-4 (1) (4)))/(2 (1))`
`= (6pm sqrt(36-16))/(2)`
`= (6pm sqrt20)/(2)`
This doesn't resemble any of the answer choices, so continue simplifying:
`(6pm sqrt20)/(2)`
`= (6pmsqrt4 sqrt5)/(2)`
`= (6 pm2 sqrt5)/(2)`
`=6/2 pm (2 sqrt5)/(2)`
`=3 pm sqrt5`
Hence, (A) is correct.