Question

How do I find the discriminant of a quadratic equation?

Answer 1

The discriminant is the bit under the radical, the $b^2-4ac$.

Because it's under a radical, it's what tells you how many and what kind of solutions you have (two real, one real, or two imaginary/complex solutions).

Does that answer your question?  Or do you need an example?

Suppose you had the equation $3x^2-7x+1 = 0$, then you'd have:

    $a=3$, $b=-7,$ and $c=1$

You'd plug those values into $b^2-4ac$ to see if the discriminant was positive, zero, or negative:

    $\begin{aligned}b^2-4ac &= (-7)^2-4(3)(1) \\&= 49 - 12 \\&= 37\endaligned}$

Since that is 37 (a postiive number), you'd have two real solutions.