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# What 2 numbers add up to get 17 and multiply to get 42??

$x_{1,2} = \frac{ -17 \pm \sqrt{ 17 ^2 - 4 \cdot 1 \cdot 42} }{ 2 \cdot 1 }$ $x_{1,2} = \frac{ -17 \pm \sqrt{ 121 } }{ 2 }$ $x_1 = \frac{ -17~+~\sqrt{ 121 } }{ 2 } = -3$ $x_2 = \frac{ -17~-~\sqrt{ 121 } }{ 2 } = -14$ And so $x^2+17x+42 = (x+3)(x+14) \to x = -3, -14$ But that is what x equals to when you solve it, but by doing it this way we just have to give the opposite sign to the numbers. So the two numbers are 3 and 14. They add to 17 and multiply to 42. Hope that helped :)