Using The Quadratic Equation

Objectives • We will understand why factorising cannot be used to solve every Quadratic Equation • We should memorise the formula which will solve ALL quadratic equations • We should be able to use the Quadratic formula to solve Quadratics with integer solutions • We could be able to use the formula to solve Quadratic equations which do not have integer solutions

Review of last lesson: • Use factorisation to solve this quadratic equation: x2 – x - 30 = 0 x = 6 & -5

The Quadratic Formula Factorisation will not always work when we are trying to solve a Quadratic... e.g. Try to factorise this equation: x2 + 5x + 3 = 0 There are no pairs of numbers which will multiply to make 3 and add to make 5...?? The answers to the equation are not

The Quadratic Formula There is a formula which we can substitute numbers into to get the answer though... It is important that you learn it so that you are confident about how to use it...

-b ± √ b2 - 4ac 2a

The Quadratic Formula -b ±

√b2 – 4ac 2a

Where

a = the x2 coefficient b = the x coefficient c = the constant term

Back to the question from before... x2 + 5x + 3 = 0 -b ±

√b2 – 4ac 2a

Where a = the

x2

coefficient

b = the x coefficient c = the constant term

=1 =5 =3

Tips! • Copy the equation VERY carefully until you know it accurately • Write the values of a, b and c clearly so you don’t get muddled • Write the formula out once with the substitutions in, before you have done any of the calculations • Try to lay it out the way I have on the board, you can reduce the stages as you get better at it...

Your turn... 1. x2 – 8x + 7 = 0 x=7&1 4. x2 + 6x + 3 = 0 x = -0.55 & -5.45 7. x2 + 3x - 9 = 0 x = 1.85 & -4.85

Learn that formula! Say it to yourself in your head... • Minus B, • Plus or Minus, • The Square root of: • B squared minus 4AC • ALL over 2A!!! ...Or say it out loud!?!