Question

What are the solutions of the quadratic equation below?

2x2 - 2x - 9 = 0

Answer 1

Answer: Option C

The solutions of the quadratic equation are:

`x = (1\±√(19))/(2)`

Explanation:

Use the quadratic formula to solve this equation.

For a quadratic function of the form
`ax^2 +bx +c=0` the quadratic formula is:

`x = (-b\±√(b^2-4ac))/(2a)`

In this case:

`a=2\\b=-2\\c=-9`

So

`x = (-(-2)\±√((-2)^2-4(2)(-9)))/(2(2))`

`x = (1\±√(19))/(2)`

Answer 2

For this case we must find the solutions of the following quadratic equation:

`2x ^ 2-2x-9 = 0`

The roots will come from:

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

Where:

`a = 2\\b = -2\\c = -9`

Substituting:

`x = \frac {- (- 2) \pm \sqrt {(- 2) ^ 2-4 (2) (- 9)}} {2 (2)}\\x = \frac {2 \pm \sqrt {4 + 72}} {2 (2)}\\x = \frac {2 \pm \sqrt {76}} {4}\\x = \frac {2 \pm \sqrt {2 ^ 2 * 19}} {4}\\x = \frac {2 \pm2 \sqrt {19}} {4}`

The roots are:

`x_ {1} = \frac {2 + 2 \sqrt {19}} {4} = \frac {1+ \sqrt {19}} {2}\\x_ {2} = \frac {2-2 \sqrt {19}} {4} = \frac {1- \sqrt {19}} {2}`

Answer:

Option C