what two number when multipled equal 10 but when added equal -4

Question

I do not know what two numbers fit in this equation....somebody please help!!!

Answer 1

Let a and b be the numbers, so ab=10 and a+b=-4. Substitute b=-4-a in the product: -a(4+a)=10 and -4a-a^2=10. Therefore a^2+4a+10=0. This quadratic has no real roots but we can calculate its complex roots using the formula: (-4+sqrt(16-40))/2=-2+sqrt(6)*i where i is the imaginary square of -1. The two numbers are -2+isqrt(6) and -2-isqrt(6). If we add these together we get -4 and if we multiply them we get 4+6=10.