Discriminant analysis Practice Questions (Grade 9)

Discriminant analysis. Game on.

Discriminant analysis is a grade 9 math skill aligned to Common Core standard HSA.REI.B.4: solve quadratic equations in one variable. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 discriminant analysis problems our math games drill.

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Warm-upeasy

How many distinct real roots does $x^{2} - 9 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = -9$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(-9) = 36\textsf{,}$ so there are $2$ distinct real roots.

Mid-gameeasy

How many distinct real roots does $x^{2} + 2x + 10 = 0$ have?

Here $a = 1$ , $b = 2$ , and $c = 10$ . Substituting into $b^{2} - 4ac$ gives $2^{2} - 4(1)(10) = -36\textsf{,}$ so there are $0$ distinct real roots.

Mid-gameeasy

How many distinct real roots does $x^{2} - 6x + 9 = 0$ have?

Here $a = 1$ , $b = -6$ , and $c = 9$ . Substituting into $b^{2} - 4ac$ gives $(-6)^{2} - 4(1)(9) = 0\textsf{,}$ so there is exactly $1$ distinct real root.

Mid-gameeasy

How many distinct real roots does $x^{2} - 25 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = -25$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(-25) = 100\textsf{,}$ so there are $2$ distinct real roots.

Mid-gameeasy

How many distinct real roots does $x^{2} + 1 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = 1$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(1) = -4\textsf{,}$ so there are $0$ distinct real roots.

Mid-gameeasy

How many distinct real roots does $x^{2} - 10x + 25 = 0$ have?

Here $a = 1$ , $b = -10$ , and $c = 25$ . Substituting into $b^{2} - 4ac$ gives $(-10)^{2} - 4(1)(25) = 0\textsf{,}$ so there is exactly $1$ distinct real root.

Mid-gameeasy

How many distinct real roots does $x^{2} - 49 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = -49$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(-49) = 196\textsf{,}$ so there are $2$ distinct real roots.

Buzzer beatereasy

How many distinct real roots does $x^{2} + 9 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = 9$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(9) = -36\textsf{,}$ so there are $0$ distinct real roots.

Discriminant analysis. Game on.

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