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
Example 2. Solve 4x2 − 11x + 6 = 0
Example 3. Solve 2x2 + 2x − 24 = 0
Example 4. Solve 3x2 − 4x − 20 = 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
| 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
| 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
| 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: 
