Question

What can be said about the discriminant of the graph below?

A The discriminant is positive, so there are no solutions.
B. The discriminant is 0, so there is one solution.
C. The discriminant is negative, so there are no solutions.
D. The discriminant is positive, so there are 2 solutions.

Answer 1

The discriminant is negative, so there are no solutions ⇒ C

Explanation:

The discriminant is used to know the number and the type of the roots of the quadratic equation without solving it

1. If the value of the discriminant is positive, then the equation has 2 solutions, which means the parabola intersects the x-axis in 2 points
2. If the value of the discriminant is zero, then the equation has 1 solution, which means the parabola intersects the x-axis in 1 point
3. If the value of the discriminant is negative, then the equation has no solutions, which means the parabola does not intersect the x-axis

Let us solve the question

In the given figure

∵ The parabola represents the quadratic equation

∵ The parabola does not intersect the x-axis

→ That means there are no solutions

∴ The equation has no solutions

→ By using the 3rd rule above

∴ The discriminant is negative

∴ The discriminant is negative, so there are no solutions