Solving Quadratic Equations The Theory If one side = 0 Then if a X b = 0 a= 0 or b = 0 We use this to solve quadratic Equations

We must first factorise x2 – 5x = 0 Common Factor x(x – 5) = 0 Using Theory x = 0 or Solutions x = 0 or x – 5 = 0 x = 5 also known as roots

If there is no common factor must be difference of 2 squares or trinomial x2 – 2x – 15 = 0 Trinomial (x )(x ) = 0 (2 thingies) (3 thingies) – 3 + – 5 + + 3 – 5 or x – 5 = 0 x + 3 = 0 solutions x = -3 or x = 5

Sometimes it is difficult to factorise. Sometimes it is impossible! Luckily we have a formula to solve any quadratic equation. However!!!!!!!!!

The Quadratic Formula To Solve Equation ax2 + bx + c = 0 x = + -b √ b2 – 4ac – 2a Not on Formula Sheet

Solve 3x2 – 8x + 2 = 0 ax2 + bx + c = 0 + -b a = 3 b = -8 c = 2 x = √ b2 – 4ac – 2a + 8 √ 82 – 4X3X2 – 2X3 Beware when using calculator + 8 √ 40 – 6 8 + √ 40 8 – OR √ 40 6 6 = 2.39 or = 0.28

Sometimes quadratic equations are disguised x2 - 3x + 4 = 0

O x (x + 5) = - 10 Quadratic? No x2 However, breaking brackets Quadratic Equation Must make equal to zero x2 + 5x + 10 = Now factorise or Quadratic Formula No x2 O

Completing Square method x2 – 6x + 5 = 0 (x – 3)2 – 9 + 5 = 0 (x – 3)2 – 4 = 0 (x – 3)2 = 4 (x – 3) = √4 x – 3 = 2 x = 5 or x – 3 = -2 or x = 1