Find the set of values of k for which x^2 + 2x+11 = k(2x-1)

The discriminant for a quadratic polynomial of the form f(x) = ax^2 + bx + c is given by b^2 - 4ac. If the discriminant is strictly greater than 2, the quadratic has 2 real distinct roots, i.e 2 unique x-values for which f(x) = 0. This fact can be used to solve the question. First of all, rearrange the above quadratic and equate to 0. Next use the equation of the discriminant to get a polynomial in k. Find the critical values of k and hence calculate the constraints on k. (1) X^2 + (2-2K)X + (11+K) = 0; (2) 4k^2 - 12k - 40 > 0, k^2 - 4k - 10 > 0; (3) k < -2, k > 5