Question

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

Answer 1

ANSWER

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

or

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

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,

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

$x = \frac{ 5 \pm \sqrt{ 17} }{4}$

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

or

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