+162 Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.
+1804 Having a double root means that the descriminant of the quadratic is 0.
Let's simplify the equation.
Combining all like terms and simplifying, we have
\(x^2 + 15x + k \)
Now, since the descriminant is 0, we have the equation
\(15^2 - 4 (1)(k) = 0 \\ 225 - 4k = 0\\ 225 = 4k \\ k = 225 / 4 \)
Thus, our final answer is 225/4.
Thanks! :)
