The discriminant of a quadratic equation is given by
�
2
−
4
�
�
b
2
−4ac.
Explain in your own words why a quadratic equation has...
...two real solutions if the discriminant is positive
...one real solution if the discriminant is zero
...no real solutions if the discriminant is negative
[Hint: think about the quadratic formula]
The quadratic formula is used to find the solutions of a quadratic equation. It involves taking the square root of the discriminant, which is the part of the formula under the square root symbol.
If the discriminant is positive, then the square root of the discriminant is a positive number. This means that the quadratic formula will have two solutions, one with a plus sign and one with a minus sign. Therefore, the quadratic equation will have two real solutions.
If the discriminant is zero, then the square root of the discriminant is zero. This means that the quadratic formula will have only one solution, which is the same for both the plus and minus signs. Therefore, the quadratic equation will have one real solution.
If the discriminant is negative, then the square root of the discriminant is an imaginary number. This means that the quadratic formula will have two complex solutions, which cannot be expressed as real numbers. Therefore, the quadratic equation will have no real solutions.