https://static.k12.com/eli/bb/1211/5_68981/1_124249_20_69001/fd27e95748792f7c2f1d1f347a2cd56e6750b95d/media/7c533c33854b5d80d74ef525470a41d5dc1f7aba/AAHS_M5S5L8_1_teacher_graded_assignment_PROJECTGUIDE.pdf sorry for the copy paste thing. Anyone know these?

Question

whpalmer4 · Answer

If you have a quadratic:
$$ax^2 + bx + c=0,\ a\ne 0$$the discriminant ($\Delta$) is given by $$\Delta = b^2-4ac$$If you are thinking that looks like the expression under the square root sign in the quadratic formula, give yourself a pat on the back.

With the discriminant, we can predict the form of the solutions to the quadratic.

$$\Delta > 0$$we will have 2 real solutions

For example: $$x^2 -4 = 0$$$$a=1,\ b=0,\ c=-4,\ \Delta = 0^2-4(1)(-4) = 16$$solutions are $x=2,\ x=-2$

$$\Delta <0$$we will have a complex conjugate pair of solutions of form $a\pm bi$ where $i = \sqrt{-1}$
For example:
$$x^2 + 1 = 0$$$$0^2-4(1)(1) = -4$$
Solutions are $x = 0+i$, $x = 0-i$

Final case is $$\Delta = 0$$Here we have two real solutions, but they are identical.
For example:$$x^2 = 0$$Discriminant is $\Delta = 0^2-4(0)(0) = 0$ 
Solutions are $x = 0$ and $x = 0$.