Everything Maths Grade 11

7.2 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS

We see that sv =− 12 and s + 2v =− 5. This is a set of simultaneous equations

in s and v, but it is easy to solvenumerically. All the options for s and v are

considered below.

s v s + 2v

2 − 6 − 10

− 2 6 10

3 − 4 − 5

− 3 4 5

4 − 3 − 2

− 4 3 2

6 − 2 2

− 6 2 − 2

We see that the combination s = 3 and v =− 4 gives s + 2v =− 5.

Step 4 : Write the equation with factors

(2x + 3)(x− 4) = 0

Step 5 : Solve the equation

If two brackets are multiplied together and give0, then one of the brackets must

be 0, therefore

2 x + 3 = 0

or

x− 4 = 0

Therefore, x =−^32 or x = 4

Step 6 : Write the final answer

The solutions to 2 x^2 − 5 x− 12 = 0 are x =−^32 or x = 4.

It is important to remember that a quadratic equation has to be in the form ax^2 + bx + c = 0 before
one can solve it using the factorisation method.

Example 2: Solving quadratic equation by factorisation

QUESTION

Solve for a: a(a− 3) = 10

SOLUTION

Step 1 : Rewrite the equation inthe form ax^2 + bx + c = 0

Remove the brackets and move all terms to oneside.