+1234 Find the constant $k$ such that the quadratic $2x^2 + 3x + 8x + k - x^2 + 20x$ has a double root.
+129771 2x^2 + 3x + 8x + k - x^2 + 20x simplify
x^2 + 31x + k
To have a double root, the discriminant must = 0
So
31^2 - 4 (1)k = 0
961 - 4k = 0
961 = 4k
k = 961 / 4
+36943 Simplify to
x^2 + 31x + k now complete the square for 'x'
(x+ 15.5)^2 - 240.25 + k will have a double root at x = -15.5 when k = 240.25
