Use the discriminant of the quadratic polynomial to find the number of (real) roots.
The quadratic functions are generally in the form f(x)=Ax2+Bx+C. The zeroes of this function is then the solution to the equation Ax2+Bx+C=0.(where A≠0)
Hence we try to solve this equation.
If you try to solve the equation (just like you'd solve a linear equation), you'd run into trouble when you realize that the xs can't be as easily isolated like in the case with linear equations. So we use a different approach, what is called the "completion of squares".
If you are familiar with the method of "completing the squares" (and it isn't very difficult,) you'd know that our goal is to somehow "arrange" the equation in the form (linear binomial)2+constant term. When you arrange the equation in this way, isolating the xs is very easy. I'll not show you the entire process of completing the square for our given function but I presume that you are somewhat familiar with it (if not, I suggest you look it up on the internet).
The end result of our method will yield a very familiar expression, what we are used to calling as the "quadratic formula". You should end up with something like this:
x=−B2⋅A± √(B2−4⋅A⋅C)/√2⋅A
where A, B and C are the coeffients of our function f(x).
