+1577 Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.
+1944 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! :)
