How to find the discriminant?
Before we learn how to find the discriminantquadratic equation of the form ax2 + bx + c = 0 and how to find the roots of the given equation, we need to recall the definition of the quadratic equation. An equation of the form ax2 + bx + c = 0 (where a, b and c are any numbers, we also need to remember that a ≠ 0) is square. All the quadratic equations will be divided into three categories:
- those who do not have roots;
- there is one root in the equation;
- there are two roots.
In order to determine the number of roots in the equation, we need a discriminant.
How to find the discriminant. Formula
We are given: ax2 + bx + c = 0.
The discriminant formula: D = b2 - 4ac.
How to find the roots of the discriminant
The sign of the discriminant determines the number of roots:
- D <0, there are no roots;
- D = 0, the equation has one root;
- D> 0, the equation has two roots.
The roots of the quadratic equation are found by the following formula:
X1 = -b + √D / 2a; X2 = -b + √D / 2a.
If D = 0, then you can safely use anyfrom the presented formulas. You will get the same answer in any case. And if it turns out that D> 0, then you do not have to count anything, since the equation has no roots.
I must say that finding a discriminant is notso it's hard if you know the formulas and carefully calculate. Sometimes there are errors when substituting negative numbers in the formula (you need to remember that minus a minus gives a plus). Be careful, and it will work out!
