Quadratics

Question 1

What is the general form of a quadratic?

Answer 1

ax² + bx + c

Question 2

How do you factorise when ‘a’ has more than two factors?

Answer 2

Look for two numbers which add to make ‘b’ and multiply to make ‘ac’

eg. 2x² + 7x + 3

a = 2, b = 7, c = 3

Find two numbers which:

+ to make 7 6 and 1

x to make 6

Factorise in pairs:

2x² + 6x | x + 3 —> 2x(x + 3) + 1(x + 3)

Tidy up:

The numbers that you are using to multiply the brackets by (2x and 1) become one of the brackets. The other is the bracket in common (x + 3).

so: (2x + 3)(4x -1) is the answer

Question 3

How does one solve quadratic equation?

Answer 3

If the equation does not already =0, make it =0

Then, factorise the equation.

Then, find x based in the fact that x + the number in each bracket must = 0!

eg. x² + 11x + 30 = 12

x² + 11x + 18 = 0

= (x + 2)(x + 9)

x = -2 OR x = -9