Discriminant worksheet

One calculation that tells you what the answers will look like before you find them: how many there are, and whether they are whole, fractional or irrational.



Sigma Prep · sigmaprep.io/worksheets Name The Discriminant Date Period Find the discriminant and describe the solutions. Find the discriminant: $a^{2} + 14 a + 15 = 0$ Find the discriminant: $4 a^{2} - 14 a - 16 = 0$ Find the discriminant: $3 n^{2} - 10 n - 13 = 0$ Find the discriminant: $4 m^{2} - 10 m - 16 = 0$ Find the discriminant: $4 v^{2} - 11 v + 17 = 0$ Find the discriminant: $r^{2} + 12 r + 20 = 0$ Find the discriminant: $4 b^{2} - 11 b - 14 = 0$ Find the discriminant: $4 n^{2} + 10 n - 13 = 0$ Find the discriminant: $5 a^{2} - 14 a + 16 = 0$ Find the discriminant: $4 m^{2} + 14 m + 20 = 0$ Find the discriminant: $5 k^{2} - 10 k + 15 = 0$ Find the discriminant: $3 k^{2} + 13 k - 18 = 0$ Find the discriminant: $y^{2} + 10 y - 13 = 0$ Find the discriminant: $2 p^{2} + 12 p + 13 = 0$ Find the discriminant: $5 k^{2} - 10 k - 20 = 0$ Find the discriminant: $b^{2} + 12 b - 13 = 0$ Find the discriminant: $n^{2} - 13 n + 13 = 0$ Find the discriminant: $3 v^{2} - 13 v - 20 = 0$ Find the discriminant: $5 y^{2} - 10 y - 20 = 0$ Find the discriminant: $4 m^{2} + 10 m - 19 = 0$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Discriminant

Date Period

Find the discriminant and describe the solutions.

Find the discriminant: $a^{2} + 14 a + 15 = 0$
Find the discriminant: $4 a^{2} - 14 a - 16 = 0$
Find the discriminant: $3 n^{2} - 10 n - 13 = 0$
Find the discriminant: $4 m^{2} - 10 m - 16 = 0$
Find the discriminant: $4 v^{2} - 11 v + 17 = 0$
Find the discriminant: $r^{2} + 12 r + 20 = 0$
Find the discriminant: $4 b^{2} - 11 b - 14 = 0$
Find the discriminant: $4 n^{2} + 10 n - 13 = 0$
Find the discriminant: $5 a^{2} - 14 a + 16 = 0$
Find the discriminant: $4 m^{2} + 14 m + 20 = 0$
Find the discriminant: $5 k^{2} - 10 k + 15 = 0$
Find the discriminant: $3 k^{2} + 13 k - 18 = 0$
Find the discriminant: $y^{2} + 10 y - 13 = 0$
Find the discriminant: $2 p^{2} + 12 p + 13 = 0$
Find the discriminant: $5 k^{2} - 10 k - 20 = 0$
Find the discriminant: $b^{2} + 12 b - 13 = 0$
Find the discriminant: $n^{2} - 13 n + 13 = 0$
Find the discriminant: $3 v^{2} - 13 v - 20 = 0$
Find the discriminant: $5 y^{2} - 10 y - 20 = 0$
Find the discriminant: $4 m^{2} + 10 m - 19 = 0$



Sigma Prep · sigmaprep.io/worksheets Name The DiscriminantAnswer keyVersion 1 Date Period Find the discriminant and describe the solutions. Find the discriminant: $a^{2} + 14 a + 15 = 0$ $136$ , two irrational solutions Find the discriminant: $4 a^{2} - 14 a - 16 = 0$ $452$ , two irrational solutions Find the discriminant: $3 n^{2} - 10 n - 13 = 0$ $256$ , two rational solutions Find the discriminant: $4 m^{2} - 10 m - 16 = 0$ $356$ , two irrational solutions Find the discriminant: $4 v^{2} - 11 v + 17 = 0$ $- 151$ , no real solutions Find the discriminant: $r^{2} + 12 r + 20 = 0$ $64$ , two rational solutions Find the discriminant: $4 b^{2} - 11 b - 14 = 0$ $345$ , two irrational solutions Find the discriminant: $4 n^{2} + 10 n - 13 = 0$ $308$ , two irrational solutions Find the discriminant: $5 a^{2} - 14 a + 16 = 0$ $- 124$ , no real solutions Find the discriminant: $4 m^{2} + 14 m + 20 = 0$ $- 124$ , no real solutions Find the discriminant: $5 k^{2} - 10 k + 15 = 0$ $- 200$ , no real solutions Find the discriminant: $3 k^{2} + 13 k - 18 = 0$ $385$ , two irrational solutions Find the discriminant: $y^{2} + 10 y - 13 = 0$ $152$ , two irrational solutions Find the discriminant: $2 p^{2} + 12 p + 13 = 0$ $40$ , two irrational solutions Find the discriminant: $5 k^{2} - 10 k - 20 = 0$ $500$ , two irrational solutions Find the discriminant: $b^{2} + 12 b - 13 = 0$ $196$ , two rational solutions Find the discriminant: $n^{2} - 13 n + 13 = 0$ $117$ , two irrational solutions Find the discriminant: $3 v^{2} - 13 v - 20 = 0$ $409$ , two irrational solutions Find the discriminant: $5 y^{2} - 10 y - 20 = 0$ $500$ , two irrational solutions Find the discriminant: $4 m^{2} + 10 m - 19 = 0$ $404$ , two irrational solutions Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The DiscriminantAnswer keyVersion 1

Date Period

Find the discriminant and describe the solutions.

Find the discriminant: $a^{2} + 14 a + 15 = 0$ $136$ , two irrational solutions
Find the discriminant: $4 a^{2} - 14 a - 16 = 0$ $452$ , two irrational solutions
Find the discriminant: $3 n^{2} - 10 n - 13 = 0$ $256$ , two rational solutions
Find the discriminant: $4 m^{2} - 10 m - 16 = 0$ $356$ , two irrational solutions
Find the discriminant: $4 v^{2} - 11 v + 17 = 0$ $- 151$ , no real solutions
Find the discriminant: $r^{2} + 12 r + 20 = 0$ $64$ , two rational solutions
Find the discriminant: $4 b^{2} - 11 b - 14 = 0$ $345$ , two irrational solutions
Find the discriminant: $4 n^{2} + 10 n - 13 = 0$ $308$ , two irrational solutions
Find the discriminant: $5 a^{2} - 14 a + 16 = 0$ $- 124$ , no real solutions
Find the discriminant: $4 m^{2} + 14 m + 20 = 0$ $- 124$ , no real solutions
Find the discriminant: $5 k^{2} - 10 k + 15 = 0$ $- 200$ , no real solutions
Find the discriminant: $3 k^{2} + 13 k - 18 = 0$ $385$ , two irrational solutions
Find the discriminant: $y^{2} + 10 y - 13 = 0$ $152$ , two irrational solutions
Find the discriminant: $2 p^{2} + 12 p + 13 = 0$ $40$ , two irrational solutions
Find the discriminant: $5 k^{2} - 10 k - 20 = 0$ $500$ , two irrational solutions
Find the discriminant: $b^{2} + 12 b - 13 = 0$ $196$ , two rational solutions
Find the discriminant: $n^{2} - 13 n + 13 = 0$ $117$ , two irrational solutions
Find the discriminant: $3 v^{2} - 13 v - 20 = 0$ $409$ , two irrational solutions
Find the discriminant: $5 y^{2} - 10 y - 20 = 0$ $500$ , two irrational solutions
Find the discriminant: $4 m^{2} + 10 m - 19 = 0$ $404$ , two irrational solutions

How to do these

Find the discriminant: $2 x^{2} + 5 x + 1 = 0$

a = 2, b = 5, c = 1.
b² - 4ac is 25 - 8.
It is positive but not a perfect square.

The answer is $17$ , two irrational solutions.

Where students go wrong

Dropping the sign of b before squaring. b² is positive whatever b was, so a negative b changes nothing here. What does matter is the sign of c: a negative c makes -4ac positive and the discriminant is guaranteed positive.

Also called the nature of the roots or b squared minus 4ac.

Questions about these worksheets

Yes. Every discriminant sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the discriminant questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Discriminant worksheet

The Discriminant

The DiscriminantAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these discriminant worksheets free?+

Do the discriminant worksheets come with an answer key?+

Are these discriminant worksheets printable?+

What grade are these discriminant worksheets for?+

Can I get a different version of the same discriminant worksheet?+

Is this a free alternative to Kuta Software for discriminant?+

Can I choose how hard the discriminant questions are?+

What do students get wrong with discriminant?+