A2400 ch2m | Version 1.1 | September 2020
The discriminant: equal 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 x2 + 3pq + p = 0, where is a non-zero constant, has equal roots.
Find the value of p.
2 The equation x2 + 2px + (3p + 4) = 0, where p is a positive constant, has equal roots.
(a) Find the value of p.
(b) For this value of p, solve the equation x2 + 2px + (3p + 4) = 0.
3 Given that the equation kx2 + 12x + k = 0, where k is a positive constant, has equal roots, find
the value of k.
