Question 155144

A quadratic polynomial can have 2 real solutions, 1 real solution, or 2 complex solutions. To determine whether the solutions are real or complex, simply use the discriminant formula. 


For example, to see if the equation {{{2x^2+6x-10}}} has real or complex solutions, let's use the discriminant formula




From {{{2x^2+6x-10}}} we can see that {{{a=2}}}, {{{b=6}}}, and {{{c=-10}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(6)^2-4(2)(-10)}}} Plug in a=2, b=6, and c=-10



{{{D=36-4(2)(-10)}}} Square 6 to get 36



{{{D=36--80}}} Multiply 4(2)(-10) to get (8)(-10)=-80



{{{D=36+80}}} Rewrite D=36--80 as D=36+80



{{{D=116}}} Add 36 to 80 to get 116



Since the discriminant is greater than zero, this means that there are two real solutions. So the quadratic has two real solutions