+3 Find the discriminant of the quadratic \(5x^2-2x+8\).
Find all the solutions to \(\frac{x+4}{x+5} = \frac{x-5}{2x}\)
+781 1. The discriminant of a quadratic is b^2-4ac.
In the equation 5x^2-2x+8, a=5, b= -2, c=8. So plugging in the values of the variables, b^2-4ac=(-2)^2-4(5)(8)=4-160= -156.
2.
\(\frac{x+4}{x+5}=\frac{x-5}{2x}\\ 2x^2+8x=x^2-25\\ x^2+8x+25=0\)
Now we just have a quadratic equation and we solve to get \(x=-4+3i, -4-3i\).
