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D2. Elementary algebra
Solving quadratic equations

Vocabulary Any equation formed using a quadratic function, such as x2 + 7x - 11 = 0, is called a quadratic equation All these equations are quadratic equations: x2 - 12x = 4, x2 + 14 = x, 6x2 + x - 1 = 0, 5 - x2 = 0 Generally, quadratic equations have the form: ax2 + bx + c=0, where a, b and c are numbers and a ¹ 0 A quadratic equation like x2 + 3x + 2=0 can be solved by factorising. Because x2 + 3x + 2=(x + 1)(x + 2) we can write the quadratic equation as: (x + 1)(x + 2)=0 Now we know that either (x + 1) = 0 or (x + 2) = 0. So the two solutions to the equation are -1 and -2. Example: solve x² + 4x + 3=0 Step 1: Factorise (x + 3)(x + 1)=0 Step 2: Write down the two solutions: -3 and -1 Step 3: Check your answers fit the original equation   Example: Solve x² - 2x - 3=0 Step 1: Factorise (x + 1)(x - 3)=0 Step 2: Write down the two solutions: -1 and 3 Step 3: Check your answers fit the original equation

Practise solving quadratic equations. You may find this hard to do in your head, but try anyway. Or you could write down the factorised form of the quadratic expression. Press "Solve" to get started and try to get 10 correct answers at least before you move on.

x² + x + =0 x=  or x= Coded:

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