Grade 9 · Algebra & functions

Discriminant analysis practice

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.

CCSS HSA.REI.B.415 questions in the bank

Sample questions

Try 8 for free

Question 1easy

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

$x^2 - 9 = (x - 3)(x + 3) = 0$ , giving $x = 3$ and $x = -3$ . That is $2$ distinct real roots.

Question 2easy

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

Discriminant $= 2^2 - 4(1)(10) = 4 - 40 = -36 < 0$ . No real roots, so the answer is $0$ .

Question 3easy

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

$x^2 - 6x + 9 = (x - 3)^2 = 0$ , so there is exactly $1$ repeated root.

Question 4easy

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

$x^2 - 25 = (x - 5)(x + 5) = 0$ , giving $x = 5$ and $x = -5$ : $2$ distinct real roots.

Question 5easy

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

$x^2 = -1$ has no real solution because a square cannot be negative. The answer is $0$ .

Question 6easy

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

$x^2 - 10x + 25 = (x - 5)^2 = 0$ , so there is exactly $1$ repeated root.

Question 7easy

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

$x^2 - 49 = (x - 7)(x + 7) = 0$ , giving $2$ distinct real roots.

Question 8easy

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

$x^2 = -9$ has no real solution, so the answer is $0$ .

Tests that cover discriminant analysis:

SAT PSAT 8/9 NAEP LEAP 2025 NY State Math

More Grade 9 skills:

Statistics basics Compound inequality situations Equivalent rational expressions (SAT)Problem solving in context (SAT)Common factor factoring (SAT)Evaluating functions at a value Interpreting data displays Absolute value equations All Grade 9 practice →

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