Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

parmen Jul 10, 2024

#1**+1 **

First, let's combine all like terms and simplify. We have

\(x^2 + 15x + k \) as the simplified version.

To have a double root means that the descriminant is 0.

The descriminant is in the form of \(b^2-4ac\), so we have the equation

\(15^2 - 4 (1)(k) = 0 \\ 225 - 4k = 0\\ 225 = 4k \\ k = 225 / 4\)

Thus, our answer is 225/4.

Thanks! :)

NotThatSmart Jul 10, 2024