Question

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

Answer 1

Answer:

$x=\frac{5+\sqrt{17}}{4}\,\,\,and\,\,\,x=\frac{5-\sqrt{17}}{4}$

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

(mark both)

Step-by-step 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:

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

$x=\frac{5+-\sqrt{25-4(2)(1)} }{2*2} \\x=\frac{5+-\sqrt{17}}{4}$

Therefore the two values are:

$x=\frac{5+\sqrt{17}}{4}\,\,\,and\,\,\,x=\frac{5-\sqrt{17}}{4}$

Answer 2

Answer:

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!

:)