Question

Select the two values of x that are roots of this equation . 2x ^ 2 + 1 = 5x

Answer 1

2x^2 + 1 = 5x

<=>

2x^2 - 5x + 1 =0

b= -5

Discriminant b^2 - 4ac = 5^2 -4 x 2 x 1 = 25 - 8 = 17

=> Option C and D are correct.

Hope this helps!

:)

Answer 2

`x=(5+√(17))/(4)\,\,\,and\,\,\,x=(5-√(17))/(4)`

which agrees with the last two options in the list of possible answers

(mark both)

Explanation:

We start by re-writing the quadratic equation in standard form:

`2x^2-5x+1=0`

Which can be solved by using the quadratic formula for a quadratic
`(ax^2+bx+c=0)`

with parameters:

`a=2,\,\,b=-5,\,\,and\,\,c=1`

`x=(5+-√(25-4(2)(1)) )/(2*2) \\x=(5+-√(17))/(4)`

Therefore the two values are:

`x=(5+√(17))/(4)\,\,\,and\,\,\,x=(5-√(17))/(4)`