Lesson

Quadratic Equations

A quadratic $ax^2 + bx + c = 0$ often factorises into two brackets. If $(x - p)(x - q) = 0$ then $x = p$ or $x = q$. The discriminant $b^2 - 4ac$ tells you how many real roots there are.

Practice

Q1

Find both roots of $x^2 - 5x + 6 = 0$.

Show hint

The factors are $(x-2)$ and $(x-3)$.

Q2

Find both roots of $x^2 - 9 = 0$.

Show hint

Remember the negative root.

When a quadratic does not factorise neatly, use the quadratic formula. The discriminant's sign decides whether the roots are real and distinct, real and repeated, or complex.

Quiz

Q1

Find both roots of $x^2 + x - 12 = 0$.

Show hint

Two numbers multiplying to $-12$ and summing to $1$.

Q2

Which value is a root of $x^2 - 4x + 4 = 0$?

Show hint

It is a perfect square, $(x-2)^2$.

Q3

What is the sign of the discriminant of $x^2 + 2x + 5$?

Show hint

Compute $b^2 - 4ac = 4 - 20$.