Cambridge International AS and A Level Mathematics Pure Mathematics 1

Algebra

P1^

1

The part of the quadratic formula which determines whether or not there are real

roots is the part under the square root sign. This is called the discriminant.

x bb ac

a

=––±

(^24)
2
If b^2 − 4 ac > 0, the equation has two real roots (see figure 1.10).
If b^2 − 4 ac < 0, the equation has no real roots (see figure 1.11).
If b^2 − 4 ac = 0, the equation has one repeated root (see figure 1.12).
The discriminant, b^2 – 4ac
x
Figure 1.10
x
Figure 1.11
x
Figure 1.12