If two things multiply to zero, one of them is zero. Use it to solve quadratic equations, and avoid the divide-by-x trap.
What you will learn
- Solve x² + bx + c = 0 by factorising
- Rearrange an equation to = 0 first
- Keep the x = 0 solution
A product that is zero
If A × B = 0, then A = 0 or B = 0.
That is the whole trick.
- x² − x − 12 = 0
- (x − 4)(x + 3) = 0
- x − 4 = 0 or x + 3 = 0
- x = 4 or x = −3
Notice the signs flip: the bracket (x + 3) gives x = −3. Put each answer back in to check: 16 − 4 − 12 = 0.
The rest of this lesson and its 6 practice questions are locked.
In this lesson
- A product that is zero
- Make one side zero first
- Forming a quadratic
- Try it: Check with the solver
6 practice questions, marked as you go; about 20 minutes in all.
In this unit: Quadratics
Expand and factorise quadratics, solve them by factorising, the formula and completing the square, and read roots and turning points from graphs.