How many roots does the equation x^2 = x + 12 have and what are they?
x2 -x -12 = 0. Here we have rearranged the equation so that we have 0 on one side of the equation, allowing us to now factorise. (x - 4)(x+3) = 0. By looking at the equation we can see that the number 12 has 3 multiplying factor couples; 1 and 12; 2 and 6; 3 and 4. The minus sign can be used interchangeably on the factor couples to produce the result of -12. Of the three couples, only one can produce a result of -x when the brackets are multiplied out. Hence the desired factor couple is +3 and -4. (x-4) = 0 or (x+3) = 0. Hence, x = 4 or x = -3. If we treat the two brackets as 'a' and 'b', the equation becomes a x b = 0. This would mean either 'a' or 'b' is 0. We can therefore use an "or" scenario to find that x is either 4 or -3. As a result, the equation has two distinct real roots, 4 and -3.
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