The solutions to

2x^2 - 10x + 13 = -6x^2 - 18x - 15

are a+bi and a-bi, where a and b are positive. What is a\cdot b?

RedDragonl Jul 11, 2024

#1**+1 **

First, let's simplify all like terms and bring all terms to one side.

We get the equation

\(2x^{2}+2x+7=0\)

Now, using the quadratic equation, we finally get two answers. We find that we have

\(x=-\frac{1}{2}+\sqrt{13}\cdot (\frac{1}{2}i)\\ x=-\frac{1}{2}-\sqrt{13}\cdot (\frac{1}{2}i)\)

Now we know what A and B are. We find that

\(a=-1/2; b = \frac{\sqrt{13}}{2}\)

Multiplying them toeghet, we finally come up with the answer.

We finally have

\(ab=-\frac{\sqrt{13}}{4}\)

Thus, our final answer is -sqrt(13)/4

Thanks! :)

NotThatSmart Jul 11, 2024