Note: The individual values = 1 and = 2 are called the roots of the equation. x x Example 2: Solve 2x = 0 x2 – Factorise: 2) = 0 x(x – Either = 0 or (x 2) = 0 x – So = 0 or = 2 x x Method 2: Using the formula Recall that the roots of the quadratic equation are given by the formula: Example 3: Solve the equation Solution: First we rearrange so that the right hand side is 0. We get We can then tell that = 2, = 3 and = -12. a b c Substituting these into the quadratic formula gives: (this is the for the solutions) surd form If we have a calculator, we can evaluate these roots to get: = 1.81 or = -3.31 x x If you need more help with the work in this chapter, there is an information booklet downloadable from this web site: EXERCISE 1) Use factorisation to solve the following equations: a) + 3x + 2 = 0 b) 3x 4 = 0 x2 x2 – – c) = 15 2x x2 – 2) Find the roots of the following equations: a) + 3x = 0 b) 4x = 0 x2 x2 – c) 4 = 0 x2 – 3) Solve the following equations either by factorising or by using the formula:
Note: The individual values x = 1 and x = 2 are called the roots of the equation. Example 2: Solve x2 – 2x = 0 Factorise: x(x – 2) = 0 Either x = 0 or (x – 2) = 0 So x = 0 or x = 2 Method 2: Using the formula Recall that the roots of the quadratic equation are given by the formula: Example 3: Solve the equation Solution: First we rearrange so that the right hand side is 0. We get We can then tell that a = 2, b = 3 and c = -12. Substituting these into the quadratic formula gives: (this is the surd form for the solutions) If we have a calculator, we can evaluate these roots to get: x = 1.81 or x = -3.31 If you need more help with the work in this chapter, there is an information booklet downloadable from this web site: EXERCISE 1) Use factorisation to solve the following equations: a) x2 + 3x + 2 = 0 b) x2 – 3x – 4 = 0 c) x2 = 15 – 2x 2) Find the roots of the following equations: a) x2 + 3x = 0 b) x2 – 4x = 0 c) 4 – x2 = 0 3) Solve the following equations either by factorising or by using the formula: