Question 329636

From {{{-3x^2+7x}}} we can see that {{{a=-3}}}, {{{b=7}}}, and {{{c=0}}}



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



{{{D=(7)^2-4(-3)(0)}}} Plug in {{{a=-3}}}, {{{b=7}}}, and {{{c=0}}}



{{{D=49-4(-3)(0)}}} Square {{{7}}} to get {{{49}}}



{{{D=49-0}}} Multiply {{{4(-3)(0)}}} to get {{{(-12)(0)=0}}}



{{{D=49}}} Subtract {{{0}}} from {{{49}}} to get {{{49}}}



So the discriminant is {{{D=49}}}



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



Note: because the discriminant is a perfect square, this means that the two solutions are rational solutions.