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How do you find the number of real solutions of $ax^2 + bx + c = 0$ using the discriminant $D = b^2 - 4ac$?

デッキ「Digital SAT Math: Algebra, Advanced Math & Geometry」の単語カード。

解答

If $D > 0$, there are 2 distinct real solutions; if $D = 0$, there is exactly 1 real solution (tangent to x-axis); if $D < 0$, there are no real solutions.

解説

On the Digital SAT, questions asking for what value of $k$ the equation has exactly one solution frequently require setting $b^2 - 4ac = 0$ and solving for $k$.

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