Question

How do you solve the quadratic equation `4x^2 - 8x + 1= 0` by using the Quadratic Formula?

Answer 1

Using quadratic formula: `(-b+-sqrt(b^2-4ac))/(2a)`

Explanation:

you assume the value
=> 4 to be your ''a''
=> -8 to be your ''b''
=> 1 to be your ''c''

Now just replace the values in the formula, and obtain your two values

-> N.B You will obtain two values (might be one positive one and the other, a negative one)

Answer 2

`x=(2+-sqrt3)/2`

Explanation:

`color(blue)(4x^2-8x+1=0`

This is a Quadratic equation (in form `ax^2+bx+c=0`)

Use Quadratic equation

`color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)`

Note: `aandb` are the coefficients of `x^2and x` and `c` is the constant number

So,

`color(purple)(a=4,b=-8,c=1`

`rarrx=(-(-8)+-sqrt(-8^2-4(4)(1)))/(2(4))`

`rarrx=(8+-sqrt(64-(16)))/(8)`

`rarrx=(8+-sqrt(48))/(8)`

`rarrx=(8+-sqrt(16*3))/(8)`

`rarrx=(8+-4sqrt3)/8`

`rarrx=(cancel8^2+-cancel4^1sqrt3)/cancel8^2`

`color(green)(rArrx=(2+-sqrt3)/2`

Remember that `+-` means "plus or minus"

Which implies that

`color(indigo)(x=((2+sqrt3)/(2),(2-sqrt3)/(2))`

If you are a bit confused with the Quadratic formula

Watch this video