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Find the discriminant of the quadratic \(5x^2-2x+8\).

Find all the solutions to \(\frac{x+4}{x+5} = \frac{x-5}{2x}\)

 Jun 19, 2020
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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  \(x=-4+3i, -4-3i\).

 Jun 20, 2020

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