Find the range of values of $k$ for which the equation
$$x^2-2kx+k^2-2k=6$$
has real roots. Find the roots in terms of $k$.
[Math] Find the range of values of k
algebra-precalculusquadratics
algebra-precalculusquadratics
Find the range of values of $k$ for which the equation
$$x^2-2kx+k^2-2k=6$$
has real roots. Find the roots in terms of $k$.
Best Answer
$$x^2-2kx+k^2-2k-6 = (x-k)^2-2k-6.$$Hence the equation has real roots iff $$ -2k-6\le 0\iff k\ge -3. $$