The information whether the discriminant is positive, negative, or zero can be used to determine the number of real solutions of a quadratic equation. However, it works both ways — the number of real solutions tells us whether the discriminant is positive, negative, or zero.
Discriminant
Number of Solutions
Positive
Two real solutions
Negative
No real solutions
Zero
One real solution
To determine whether the discriminants of the given equations are positive, negative, or zero, we will determine the number of solutions of each equation.
f(x)=0 g(x)=0 h(x)=0 j(x)=0
The solutions of these equations, if any, are the x-intercepts of the related functions, f, g, h, and j, respectively. Let's take a look at the given graph.
We can see that f has no x-intercepts, g has two x-intercepts, and h and j have one x-intercept each. Therefore, f(x)=0 has no real solutions, g(x)=0 has two real solutions, and h(x)=0 and j(x)=0 have one real solution each. Let's make a table to see what it means in terms of the dicriminants!
