Quadratic Equations

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What is the relationship between the roots and coefficients of a quadratic equation?

The sum of the roots is $-\frac{b}{a}$ and the product of the roots is $\frac{c}{a}$.

What does the 'discriminant' of a quadratic equation determine?

The discriminant $D = b^2 - 4ac$ determines the nature of the roots.

What are the possible values of the discriminant and their meanings?

If $D > 0$, there are 2 distinct real roots; if $D = 0$, there is 1 real root; if $D < 0$, there are no real roots.

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