Allday Education

Free Solving Quadratic Equations Worksheet

Ten quadratic equations with rational solutions, plus a key listing both roots of each.

Answer key included
Name: Date:
Solving Quadratic Equations
1.
x212x+36=0x^{2} - 12x + 36 = 0
2.
x23x+2=0x^{2} - 3x + 2 = 0
3.
x27x+12=0x^{2} - 7x + 12 = 0
4.
2x26x+4=02x^{2} - 6x + 4 = 0
5.
3x23x6=03x^{2} - 3x - 6 = 0
6.
3x2+9x12=03x^{2} + 9x - 12 = 0
7.
2x2+12x+10=02x^{2} + 12x + 10 = 0
8.
x24x5=0x^{2} - 4x - 5 = 0
9.
x23x4=0x^{2} - 3x - 4 = 0
10.
2x28x+8=02x^{2} - 8x + 8 = 0
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Solving Quadratic Equations
1.
x212x+36=0x^{2} - 12x + 36 = 0
Answer: x=6x = 6
2.
x23x+2=0x^{2} - 3x + 2 = 0
Answer: x=1,x=2x = 1, x = 2
3.
x27x+12=0x^{2} - 7x + 12 = 0
Answer: x=3,x=4x = 3, x = 4
4.
2x26x+4=02x^{2} - 6x + 4 = 0
Answer: x=1,x=2x = 1, x = 2
5.
3x23x6=03x^{2} - 3x - 6 = 0
Answer: x=1,x=2x = -1, x = 2
6.
3x2+9x12=03x^{2} + 9x - 12 = 0
Answer: x=4,x=1x = -4, x = 1
7.
2x2+12x+10=02x^{2} + 12x + 10 = 0
Answer: x=5,x=1x = -5, x = -1
8.
x24x5=0x^{2} - 4x - 5 = 0
Answer: x=1,x=5x = -1, x = 5
9.
x23x4=0x^{2} - 3x - 4 = 0
Answer: x=1,x=4x = -1, x = 4
10.
2x28x+8=02x^{2} - 8x + 8 = 0
Answer: x=2x = 2
Andy · alldayeverydaymath.com

Scroll to see all 10 problems and the answer key on its own page. Printing includes every page.

About this worksheet

These quadratics are generated from their roots, so factoring and the quadratic formula both come out clean — ideal once students know both methods and need volume. The answer key lists both solutions for quick grading.

Students shaky on the skill itself? Send them to the free lesson: Solving Quadratic Equations — explained step by step.

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