In the quadratic formula, the radicand, b2 - 4ac, is called the discriminant
of the quadratic equation ax2 + bx + c = 0.
We can use the discriminant to determine the nature of the solutions of a
quadratic equation without having to solve the equation.
|b2 - 4ac > 0
||two different real numbers
|b2 - 4ac = 0
||two identical real numbers
|b2 - 4ac < 0
||no real number solutions
If the discriminant is a perfect square, the
solutions will not only be real numbers,
they will also be rational numbers.
Use the discriminant to determine the nature of the solutions of this
quadratic equation: -2x2 - x + 7 = 0
The discriminant is 57, a positive number.
|The equation has the form ax2 + bx + c = 0 where a
= -2, b = -1, and c = 7.
|Substitute the values of a, b, and c into the discriminant and simplify.
b2 - 4ac
|= (-1)2 - 4(-2)(7)
= 1 + 56
So the equation -2x2 - x + 7 = 0 has two unequal real number solutions.