    ### Solving quadratics of the form ax2 + bx + c = 0 by factorising first

This means find the values of x where the quadratic ax2 + bx + c = 0 This can be done as follows:

 i. Factorise ax2 + bx + c = 0 into the form (mx + n)(px + q)This has already been shown in Factorising Quadratics − 2 ii. So (mx + n)(px + q) = 0 iii. The values in either of the above brackets must equal to 0, as brackets means multiply and anything multipled by 0 is equal to 0. Either
• #### Example 1.   Solve 2x2 + 12x + 10 = 0

•  i. From example 1 in Factorising Quadratics − 2 the factors are: (2x + 2)(x + 5) ii. So (2x + 2)(x + 5) = 0
 iii. Either

Verify by putting these two values of x into 2x2 + 12x + 10

• #### Example 2.   Solve 4x2 − 11x + 6 = 0

•  i. From example 2 in Factorising Quadratics − 2 the factors are: (4x − 3)(x − 2) ii. So (4x − 3)(x − 2) = 0
 iii. Either

Check by putting these two values of x into 4x2 − 11x + 6

• #### Example 3.   Solve 2x2 + 2x − 24 = 0

•  i. From example 3 in Factorising Quadratics − 2 the factors are: (2x − 6)(x + 4) ii. So (2x − 6)(x + 4) = 0
 iii. Either

Verify by putting these two values of x into 2x2 + 2x − 24

• #### Example 4.   Solve 3x2 − 4x − 20 = 0

•  i. From example 4 in Factorising Quadratics − 2 the factors are: (3x − 10)(x + 2) ii. So (3x − 10)(x + 2) = 0
 iii. Either

Check by putting these two values of x into 3x2 − 4x − 20

#### Remember:Find the values of x where ax2 + bx + c = 0 is the same as solve ax2 + bx + c = 0 to:  