A2400 ch2n | Version 1.1 | September 2020
The discriminant: two distinct roots
A LEVEL LINKS
Scheme of work: 1b. Quadratic functions – factorising, solving, graphs and the discriminants
Key points
• A quadratic equation is an equation in the form ax2 + bx + c = 0 where a ≠ 0.
• For the quadratic function f(x) = a (x + p)2 + q, the graph of y = f(x) has a
turning point at (−p, q)
• For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant.
The value of the discriminant shows how many roots f(x) has:
- If b2 – 4ac > 0 then the quadratic function has two distinct real roots.
- If b2 – 4ac = 0 then the quadratic function has one repeated real root.
- If b2 – 4ac < 0 then the quadratic function has no real roots.
Practice questions
1 The equation kx2 + 4x + (5 − k) = 0, where k is a constant, has 2 different real solutions for x.
(a) Show that k satisfies
k2 – 5k + 4 > 0.
(b) Hence find the set of possible value of k.
2 The equation x2 + (k − 3)x + (3 − 2k) = 0, where k is a constant, has two distinct real roots.
(a) Show that k satisfies
k2 + 2k − 3 > 0
(b) Find the set of possible values of k.
