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Sarah (Parent) February 1 2017
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So x2 + 9x + 20 = 0
My preffered way of solving this equation is to factorise the equation. (Though I understand that different students may find other ways easier)
Factorisation is where the above equation is (x+a)(x+b) = 0
So if we times out (x+a)(x+b) we get
x2 + ax + bx + ab = 0
x2 + (a+b)x + ab = 0
Therefore we can equate this to the original question, so
x2 + 9x + 20 = x2 + (a+b)x + ab
so now we can see that
9 = a + b and
20 = ab
I would reccomend using trial and error (although I understand that different students may prefer other techniques).
So by trying for multiple values of a and b, we can see that they must equal 5 and 4.
x2 + 9x + 20 = (x+5)(x+4) = 0
We know that the only way of producing a 0 through multiplication is through multiplying one number by another. Therefore we know that
x+5= 0 or x+4=0
Through rearranging these equations we can conclude that x must equal -4 or -5.