The values of x such that
2x^2 - 6x + 5 = -4
are m + ni and m - ni, where m and n are positive. What is mn?
+487 $2x^2-6x+9=0$.
Using the quadratic formula, you get $x=\frac{6+\sqrt{36-72}}{4}$ and $x=\frac{6+\sqrt{36-72}}{4}$. These simplify to $x=\frac{3}{2}+6i$ and $x=\frac{3}{2}-6i$.
So mn=$\frac{3}{2}*6=3*3=\boxed{9}$
+129852 2x^2 - 6x + 5 = -4
2x^2 - 6x = -9 complete the square on x
2(x^2 - 3x + 9/4) = -9 + 9/2
2 ( x - 3/2)^2 = -18/2 + 9/2
2 ( x - 3/2)^2 = - 9/2
(x - 3/2)^2 = -9/4 take both roots
x - 3/2 = (3/2)i or x - 3/2 = -(3/2)i
x = (3/2) + (3/2)i or x = 3/2 -(3/2)i
m = n = 3/2
mn = (3/2)^2 = 9/4
+487 Ohhh, thank you so much @Cphill, I see where I went wrong, I forgot to divide by 4 when I simplified the square roots, so I got 6 instead of $\frac{6}{4}$. Thanks for helping out!
