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If x1 and x2 are the solutions to the quadratic equation and working backwards: (x-x1)*(x-x2) = x^2 - (x1+x2) x + x1*x2 so you can identify the terms of the developed form with the sum and product of the solutions.
In your specific example, I would decompose 672 knowing you want to have a product of 2 terms of opposite signs which adds up to -4
Coming to this question, you have -672 so the two factors which multiply to give 672 will have opposite signs i.e. one of them will be positive and the other will be negative. Also, their difference will be 4 i.e. very small. Try and split 672 into its factors. We see that 672 is divisible by 4. 672 = 4*168 = 4*4*42 = 4*4*2*3*7 (We try to split the number till we get manageable factors)
Now you have to try various combinations of these factors till you get a pair with a difference of 4. Notice that the difference is very small so we need to get 2 factors which are kind of equal to each other. Say, one factor can be 7*4 and another can be 6*4. 28 and 24 actually do have a difference of 4 so we have got our 2 factors.
Do you need to solve this problem with paper and pen or can you use a calculator, program, or website?
If you need an analytical solution, or pen-and-paper, another way to attack this type of problem would be to use the Quadratic Formula (QF); there is a lot of good material about the QF on Wikipedia or MathWorld. This approach is easier if you have a calculator, but it allows for exact, algebraic, solutions.
On the other hand, if you cannot solve the problem easily, you might not have a choice but to use the QF. And if you are allowed to use a program or web applet, then you can solve the problem numerically.
For example, here is a free online applet that solves a Quadratic Equation:
Whether you use a web program, a full-blown computer program, or a pocket calculator, once you have numeric solutions root1 and root2, you could then re-state the original equation in the following form:
(t - root1)(t - root2)
If the roots are nice round numbers, that is nice but doesn't always happen. The solutions are what they are.