Question

Solve 2x^2 - 3x = 12 using the quadratic formula.

A) x = 3/4+√105/4i, x = 3/4-√105/4i
B) x = 3/4+√87/4i, x = 3/4-√87/4i
C) x = 3/4 + √87/4, x = 3/4-√87/4
D) x = 3/4 + √105/4, x = 3/4-√105/4

Answer 1

`x = (3)/(4) + ( √(105) )/(4) \: \: , \: \: \: x = (3)/(4) - ( √(105) )/(4) \\`

Explanation:

2x² - 3x - 12 = 0

Using the quadratic formula which is

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

From the question

a = 2 , b = - 3 , c = - 12

So we have

`x = \frac{ - - 3\pm \sqrt{ ({ - 3})^(2) - 4(2)( - 12)} }{2(2)} \\ = (3\pm √(9 + 96) )/(4) \\ = (3\pm √(105) )/(4) \: \: \: \: \: \:`

Separate the solutions

We have the final answer as

`x = (3)/(4) + ( √(105) )/(4) \: \: , \: \: \: x = (3)/(4) - ( √(105) )/(4) \\`

Hope this helps you