Question

Jonathan must determine the solutions of the quadratic equation 0=4x^2+3x+8 which of the following is a solution to the equation.

Answer 1

option A

Explanation:

Using quadratic formula:

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

We will have 2 solutions.

0=4x^2+3x+8 a=4 b=3 c=8

`x_(1)=\frac{-3+\sqrt{3^(2)-4*4*8} }{2*4}\\\\x_(2)=\frac{-3-\sqrt{3^(2)-4*4*8} }{2*4}`

We have:

`x_(1)=(-3+√(9-128) )/(8)\\\\x_(2)=(-3-√(9-128) )/(8)\\\\`

So

`x_(1)=(-3+√(-119) )/(8)\\\\x_(2)=(-3-√(-119) )/(8)\\`

The solutions are not real numbers.

We know:

`i=√(-1)`

We can write:

`x_(1)=(-3+i√(119) )/(8)\\\\x_(2)=(-3-i√(119) )/(8)\\`

so the option is A:

`x_(2)=(-3-i√(119) )/(8)`