How to use the discriminant of a quadratic equation to find the nature of the roots: formula, examples, and their solutions.
The qudratic formula's b2 - 4ac
is called the determinant.
It's denoted as D.
It's called the determinant because
the D determines the nature of the x values.
If D > 0 and if D is a perfect square,
then the radical sign of the formula
will be removed.
( √ ■2 = ■ )
So there are 2 rational roots.
If D > 0 and if D is not a perfect square,
then the radical sign of the formula will remain.
So there are 2 irrational roots.
If D = 0,
then the radical part is removed.
So ± sign is gone.
So there's only 1 real root.
If D < 0,
it makes the radicand (inside the radical sign) (-).
It doesn't make sense.
So there are no real roots.
D > 0 and D = 32 (a perfect square).
So this equation has 2 rational roots.
D > 0 and D is not a perfect square.
So this equation has 2 irrational roots.
D = 0.
So this equation has 1 real root.
D < 0.
So this equation has no real roots.
If you know about complex numbers,
there's another way to write the answer.
Complex roots of a quadratic equation