AssignmentGrade-9 neonGive answer pls question Characterize the properties of the solutions of a Q.E given the different forms of discriminant.A. b^2 - 4ac > 0B. b ^ 2 - 4ac > 0C. b ^ 2 - 4ac = 0D. b ^ 2 - 4ac < 0and a perfect square but not perfect square
Answer (1)
Answer: "Math • Senior High School" assignment. The question asks to characterize the properties of the solutions of a Quadratic Equation (Q.E.) given the different forms of the discriminant (b^2 - 4ac).Here's the breakdown of the properties based on the discriminant: * A. b^2 - 4ac > 0: * Property: The quadratic equation has two distinct real roots. * B. b^2 - 4ac < 0: * Property: The quadratic equation has two distinct complex (or imaginary) roots. These roots are conjugates of each other. * C. b^2 - 4ac = 0: * Property: The quadratic equation has one real root with multiplicity 2, often referred to as a "repeated real root" or "two equal real roots". * D. b^2 - 4ac < 0: (This is a duplicate of B, so the answer for B applies here as well.) * Property: The quadratic equation has two distinct complex (or imaginary) roots.The last part of the question "and a perfect square but not perfect square" seems a bit confusing or incomplete as a standalone condition. However, if it's meant to describe a specific case related to b^2 - 4ac > 0: * If b^2 - 4ac > 0 and is a perfect square: * Property: The quadratic equation has two distinct rational roots. * If b^2 - 4ac > 0 and is NOT a perfect square: * Property: The quadratic equation has two distinct irrational roots.
