Grade 11 · Mathematics
Solve quadratic equations by factorising
A quadratic equation contains a squared variable and can have two real solutions, one repeated real solution or no real solutions. For Grade 11 Mathematics revision, factorising is useful when the expression splits into simple brackets. First put the equation equal to zero, factorise, then set each factor equal to zero. Check both answers in the original equation.
Original explanation prepared with AI assistance.
Lees hierdie verduideliking in AfrikaansWhat you will practise
Factorise a monic quadratic, apply the zero-product rule and check both roots.
The method
For x² + bx + c, look for two numbers whose product is c and whose sum is b. The zero-product rule applies only when the product is zero.
Worked example
Solve x² − 5x + 6 = 0.
- The numbers −2 and −3 multiply to 6 and add to −5.
- Write (x − 2)(x − 3) = 0.
- Either x − 2 = 0 or x − 3 = 0, so x = 2 or x = 3.
- Check: 2² − 5(2) + 6 = 0 and 3² − 5(3) + 6 = 0.
Common mistake
Do not set factors equal to zero while the other side is nonzero. Move every term to one side first.
Try it yourself
Solve x² + x − 12 = 0.
Show the explained solution
The factors are (x + 4)(x − 3). Therefore x = −4 or x = 3. Substitution makes the original expression zero for both values.
Curriculum and sources
Use the official CAPS subject document and your teacher’s annual plan to confirm the sequence and scope for your class. The link below is an official reference, not evidence of DBE approval of this explanation.
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