Answer:
See solution and explanation below.
Step-by-step explanation:
Assuming that on this case our equation is this one:
[tex] ax^2 + bx + c=0[/tex]
We can use the quadratic formula in order to solve this problem. And the quadratic formula is given by:
[tex] x= \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
If the discriminant is >0 [tex] b^2 -4ac >0[/tex] we have two real solutions
And the possible two solutions are:
[tex] x_1= \frac{-b - \sqrt{b^2 -4ac}}{2a}[/tex]
[tex] x_2= \frac{-b + \sqrt{b^2 -4ac}}{2a}[/tex]
If the discriminant is equal to 0. [tex] b^2 -4ac =0[/tex] we have just one real solution:
[tex] x = \frac{-b}{2a}[/tex]
If the discriminant is lower than 0. [tex] b^2 -4ac <0[/tex] we have two imaginaty solutions.
[tex] x_1= \frac{-b - \sqrt{b^2 -4ac}i}{2a}[/tex]
[tex] x_2= \frac{-b + \sqrt{b^2 -4ac}i}{2a}[/tex]