Final answer:
The statement is conditionally true or false depending on the value of the constant k. To confirm whether the quadratic equation x² + kx + (k - 3) = 0 has two distinct real roots, the discriminant (k² - 4k + 12) must be positive.
Step-by-step explanation:
The equation x² + kx + (k - 3) = 0 is a quadratic equation, which can have two distinct real roots, one real root, or no real roots depending on the value of the discriminant (b² - 4ac). To determine whether this equation has two distinct real roots, we need to calculate the discriminant and ensure that it is greater than zero. For our equation, a = 1, b = k, and c = k - 3.
The discriminant is given by Δ = b² - 4ac. Plugging in our values, we get Δ = k² - 4(1)(k - 3) = k² - 4k + 12. For the equation to have two distinct real roots, Δ must be positive. So, if k² - 4k + 12 > 0, the original equation has two distinct real roots. Without knowing the specific value of k, we cannot definitively say whether the equation has two distinct real roots or not. Therefore, the statement is conditionally true or false depending on the value of k.