Quadratic Equations Quadratic Equations A basic quadratic equation

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Quadratic Equations

Quadratic Equations

Quadratic Equations A basic quadratic equation contains an x 2 term. Find all the

Quadratic Equations A basic quadratic equation contains an x 2 term. Find all the possible values of x from the following: 1. x 2 = 16 x = 4 or x = - 4 2. x 2 = 81 x = 9 or x = - 9 3. x 2 + 3 = 12 x = 3 or x = -3 4. x 2 – 8 = 17 x = 5 or x = - 5 Note: Nearly all Quadratic equations have two solutions.

To solve any other quadratic equation we need to use the following principle: If

To solve any other quadratic equation we need to use the following principle: If Then either, Ax. B=0 A = 0 or B = 0 Example: 1. Either If Therefore x(x – 6) = 0 x = 0 or x – 6 = 0 x– 6=0 x=6 x = 6 or x = 0

2. Either If Therefore 3. Either If Therefore x(x + 3) = 0 x

2. Either If Therefore 3. Either If Therefore x(x + 3) = 0 x = 0 or x + 3 = 0 x+3=0 x=-3 x = - 3 or x = 0 4 x(x – 7) = 0 4 x = 0 or x – 7 = 0 4 x = 0 x=0 x– 7=0 x= 7 x = 7 or x = 0

Quadratic Equations Remember: If Then either, 1. Either If or Therefore Ax. B=0 A

Quadratic Equations Remember: If Then either, 1. Either If or Therefore Ax. B=0 A = 0 or B = 0 (x – 2)(x + 4) = 0 x – 2 = 0 or x + 4 = 0 x– 2=0 x=2 x+4=0 x=-4 x = 2 or x = - 4

2. Either If or Therefore (x + 5 )(x – 7) = 0 x

2. Either If or Therefore (x + 5 )(x – 7) = 0 x + 5 = 0 or x – 7 = 0 x+5=0 x=-5 x– 7=0 x=7 x = - 5 or x = 7

QUADRATIC EQUATIONS Most quadratic equations need to be factorised first, in order to solve

QUADRATIC EQUATIONS Most quadratic equations need to be factorised first, in order to solve them using the basic principle. Remember: x 2 – 7 x = x(x – 7) x 2 + 5 x + 6 = (x + 3)(x + 2)

Solve the following by factorisation 1. x 2 – 7 x = 0 Divide

Solve the following by factorisation 1. x 2 – 7 x = 0 Divide by common factor of x x(x – 7) = 0 Either x = 0 or x – 7 = 0 x=7 So x = 0 or x = 7 2. x 2 + 3 x = 0 Divide by common factor of x x(x + 3) = 0 Either x = 0 or x + 3 = 0 x=-3 So x = 0 or x = - 3

3. 5 x 2 – 20 x = 0 Divide by common factor of

3. 5 x 2 – 20 x = 0 Divide by common factor of 5 x 5 x(x – 4) = 0 Either 5 x = 0 or x – 4 = 0 x=4 So x = 0 or x = 4

4. x 2 + 5 x + 6 = 0 Factorise into a double

4. x 2 + 5 x + 6 = 0 Factorise into a double bracket (x + 3)(x + 2) = 0 If x + 3 = 0 or x + 2 = 0 So x=-3 x=-2 x = - 3 or x = - 2 5. x 2 – 9 x + 14 = 0 Factorise into a double bracket (x – 7)(x – 2) = 0 If x – 7 = 0 or x – 2 = 0 So x = 7 or x= 2 x = 7 or x = 2