Question

Use the quadratic formula to determine the exact solutions to the equation.

2x2−5x+1=0



Enter your answers in the boxes.

x =
or x =

Answer 1

15/7 or 17/4

Explanation:

i took the quiz and got it right!

Answer 2

`x = (5)/(4) - ( √( 17) )/(4)`

or

`x = (5)/(4) + ( √( 17) )/(4)`

EXPLANATION

The given equation is:

`2 {x}^(2) - 5x + 1= 0`

Comparing this to

`a {x}^(2) + bx + c = 0`

we have a=2, b=-5, c=1

The quadratic formula is given by

`x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac} }{2a}`

We substitute the values to get,

`x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^(2) - 4(1)(2)} }{2(2)}`

`x = ( 5 \pm √( 17) )/(4)`

`x = (5)/(4) - ( √( 17) )/(4)`

or

`x = (5)/(4) + ( √( 17) )/(4)`