The equation kx^2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. Show that k satisfies k^2-5k+4>0.

This questions is a proof type question, which means that you need to get to a specific formula. Usually, these questions give you clues in order to prove it. In this case it tells you that the equation has 2 different roots. The fact that the equation given is a quadratic and that that it has 2 different roots it means that the discriminant of the equation is bigger than 0. The discriminant of a quadratic equation of the form ax^2 +bx + c = 0 is b^2-4ab. In this case a = k, b = 4 and c = 5-k. By replacing these terms we get that 16 - 4k(5-k) > 0. By expanding the brackets and rearranging we get that k^2-5k+4>0.