
Mathematics (secondary)  Secondary/KS4/GCSE (age 1415 yrs)
Q: Solve the following quadratic equation: 2x^2  5x  3 = 0
Firstly, we need to factorise the equation: We can see (and are told) that the equation is quadratic and is therefore of the form ax^2 + bx + c. In our case, a=2, b=5 and c=3. We therefore expect two pairs of brackets that look like: (?x + ?)(?x + ?).We are looking for two numbers that multiply to give a. One obvious choice is 2 and 1. We then have (2x + d)(x + e). We now need to find the two unknown numbers that give the correct values for b and c: 2xe + xd = b = 5x and de = c = 3. The second equation is solved using d, e = 1, 3 or 3, 1. We see which of these satisfies the first additional equation as well. Try d = 3, e = 1: 2x1 + x*3 = 2x  3x = 1x. This does NOT solve the equation. Try d = 1, e = 3: 2x*3 + x*1 = 6x + x = 5x. This does solve the equation. The factorised equation is: (2x + 1)(x  3) = 0 and the solutions are x=1/2 and x = 3.
Maria
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Maria
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Literae Humaniores (Bachelors)  Wadham College, Oxford University