Mathematics

Mathematics

Problem

For the quadratic equation ax2+bx+c=0ax^{2}+bx+c=0, which of the following conditions on the discriminant guarantees that the equation has two distinct real roots? a) b2−4ac=0b^{2}-4ac=0 b) b2+4ac>0b^{2}+4ac>0 c) b2−4ac>0b^{2}-4ac>0 d) b2−4ac<0b^{2}-4ac<0
Intuitive explanation

The discriminant Δ=b2−4ac\Delta = b^2 - 4ac is a single number that tells you everything about what kind of roots a quadratic has. When Δ\Delta is positive, the square root in the quadratic formula gives you two different real values; when it's zero or negative, you get either a repeated root or complex roots instead. So you're looking for the condition that keeps Δ\Delta strictly positive.

Intuitive explanation

The discriminant Δ=b2−4ac\Delta = b^2 - 4ac is a single number that tells you everything about what kind of roots a quadratic has. When Δ\Delta is positive, the square root in the quadratic formula gives you two different real values; when it's zero or negative, you get either a repeated root or complex roots instead. So you're looking for the condition that keeps Δ\Delta strictly positive.

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