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

Answer:

option A

Step-by-step 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:

$x_{1}=\frac{-3+\sqrt{9-128} }{8}\\\\x_{2}=\frac{-3-\sqrt{9-128} }{8}$

So

$x_{1}=\frac{-3+\sqrt{-119} }{8}\\\\x_{2}=\frac{-3-\sqrt{-119} }{8}$

The solutions are not real numbers.

We know:

$i=\sqrt{-1}$

We can write:

$x_{1}=\frac{-3+i\sqrt{119} }{8}\\\\x_{2}=\frac{-3-i\sqrt{119} }{8}$

so the option is A:

$x_{2}=\frac{-3-i\sqrt{119} }{8}$