The Discriminant
In National 5 you learned how to find the nature of the roots of a quadratic using the
discriminant.
−𝑏±√𝑏2 −4𝑎𝑐
The quadratic formula, 𝑥 =
can be used to find the roots of a quadratic. The
2𝑎
nature of the roots depends of the value of b2 – 4ac, under the square root sign. This is called
the discriminant.
If b2 – 4ac > 0 the quadratic has 2 real and distinct roots.
If b2 – 4ac = 0 the quadratic has real and equal roots.
If b2 – 4ac < 0 the quadratic has no real roots.
In Higher Maths you may be asked to use the discriminant to solve problems.
Example
Find the value of p given that x2 – 2x + p = 0 has no real roots.
For no real roots
b2 – 4ac < 0
(-2)2 – 4 ×1×p < 0
4 – 4p < 0
4 < 4p
1<p
p>1