We know that the equation kx2 + (2k-3) x + K-3 = 0 for X. (1) prove that the equation always has real roots; (2) when k takes which integers, the two real roots of the equation kx2 + (2k-3) x + K-3 = 0 for X are negative integers?

We know that the equation kx2 + (2k-3) x + K-3 = 0 for X. (1) prove that the equation always has real roots; (2) when k takes which integers, the two real roots of the equation kx2 + (2k-3) x + K-3 = 0 for X are negative integers?

(1) Classification discussion: if k = 0, then the equation is a univariate linear equation, that is - 3x-3 = 0, ∧ x = - 1 has roots, (1 point) if K ≠ 0, then the equation is a univariate quadratic equation, ∧ = (2k-3) 2-4k (K-3) = 9 > 0, (2 points) ∧ the equation has two unequal real roots, (3 points) to sum up, the equation always has