The discriminant of a quadratic equation is found by using the formula B^2 - 4ac. Let's break it down into simpler terms.
When we have a quadratic equation, it usually looks something like ax^2 + bx + c = 0. The discriminant helps us determine how many solutions the equation has.
If the discriminant is positive, it means that the expression B^2 - 4ac is greater than zero. When that happens, the quadratic equation will have two real solutions. This is because when we use the quadratic formula (-b ± √(B^2 - 4ac))/2a, we will get two different values for x that make the equation true.
If the discriminant is zero, it means that the expression B^2 - 4ac equals to zero. In this case, the quadratic equation will have only one real solution. When using the quadratic formula, we will get the same value for x twice. It happens when the quadratic equation has a perfect square in it.
Lastly, if the discriminant is negative, it means that the expression B^2 - 4ac is less than zero. When that occurs, the quadratic equation will have no real solutions. We will not find any real values for x when we try to solve the equation using the quadratic formula. This happens when the quadratic equation cannot be factored into real numbers.
In summary, the discriminant helps us determine the number of real solutions for a quadratic equation. Positive discriminant means two real solutions, zero discriminant means one real solution, and negative discriminant means no real solutions.
The discriminant of a quadratic equation is given by
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]
But make it look like a 10th-grader did it
1 answer