If the discriminant of a quadratic equation is greater than zero, what does it indicate?

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If the discriminant of a quadratic equation is greater than zero, what does it indicate?

The discriminant tells you how many real solutions a quadratic has. It’s Δ = b^2 − 4ac. If Δ is greater than zero, the square root term in the quadratic formula is real and nonzero, so you get two different real values for x: x = (-b + sqrt(Δ)) / (2a) and x = (-b - sqrt(Δ)) / (2a). That means the parabola crosses the x-axis at two distinct points, giving two distinct real roots. If Δ = 0 you’d get a single real root (a repeated root), and if Δ < 0 there are no real roots, only a pair of complex conjugates.

The discriminant tells you how many real solutions a quadratic has. It’s Δ = b^2 − 4ac. If Δ is greater than zero, the square root term in the quadratic formula is real and nonzero, so you get two different real values for x: x = (-b + sqrt(Δ)) / (2a) and x = (-b - sqrt(Δ)) / (2a). That means the parabola crosses the x-axis at two distinct points, giving two distinct real roots. If Δ = 0 you’d get a single real root (a repeated root), and if Δ < 0 there are no real roots, only a pair of complex conjugates.

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