CBSE · Class 10 · Mathematics · Quadratic EquationsFor what value of k does the quadratic equation kx(x - 2) + 6 = 0 have two equal roots?

First, we expand the given equation kx(x - 2) + 6 = 0 into its standard form, which yields kx² - 2kx + 6 = 0. For this quadratic equation to have two equal real roots, its discriminant must be exactly equal to zero, meaning D = b² - 4ac = 0. Substituting the coefficients a = k, b = -2k, and c = 6 gives (-2k)² - 4(k)(6) = 0, which simplifies to 4k² - 24k = 0. Factoring this out gives 4k(k - 6) = 0, yielding k = 6 since k cannot be zero.