Quadratics

Question 1

What is the quadratic formula?

Answer 1

Question 2

How would you solve:

ax² + bx + c = 0

Answer 2

Factorise the LHS. If x(y) = 0, then x = 0 or y = 0.

e.g. 3x² + 5x = 0

x(3x + 5) = 0

x = 0

or

3x + 5 = 0

Question 3

For more complicated quadratics, use the “box”.

Demonstrate on -6x² + 7x +3.

Answer 3

ac = -6 * 3 = -18

c = 7

Multiply to give -18, add to give 7.

-2, 9

THE BOX

-6x^{<strong>2</strong>} -2x

9x 3

factor out x in top left & right

-6x -2

x -6x² -2x

9x 3

now -6x * ? = 9x

• 6x -2
• x* -6x² 2x
• -3/2* 9x 3

the top and left side give you your factors.

Therefore…

-6x² + 7x +3 = (-6x - 2) (x - 3/2)