# Worksheet on Quadratic Equations

Math worksheet on quadratic equations will help the students to practice the standard form of quadratic equation. Practice the quadratic equation and learn how to solve the quadratic equation.

1. Which of the following are quadratic equations?

(a) 3 x² + 11x + 10 = 0

(b) x + $$\frac{1}{x}$$ = 4

(c) x - $$\frac{5}{x}$$ = x²

(d) 2x² - √5x + 7 = 0

(e) x² - √x - 5 = 0

(f) x² - 3x = 0

(g) x² + 1/x² = 3

(h) x (x + 1) - (x + 2) (x - 2) = -8

2. Find if the given values are the solution of the given equations.

(a) 4x² + 5x = 0;                  x = 0 and x = $$\frac{-5}{4}$$

(b) 3x² + 11x + 10 = 0;       x = $$\frac{-2}{3}$$ and x = $$\frac{-1}{3}$$

(c) 2x² - x - 9 = 0;               x = 2 and x = 3

(d) x² - x - 1 = 0 ;                x = 1 and x = -1

(e) x² - √2x - 4 = 0;             x = -2√2 and x = √2

3. Solve the following quadratic equations and find the solution.

(a) x² - 2x - 8 = 0

(b) 3x² - 13x + 12 = 0

(c) x² + x - 2 = 0

(d) 2x² + 5x + 3 = 0

(e) 9x² - 34x - 8 = 0

(f) 10x - $$\frac{1}{x}$$ = 3

(g) (x² - 1)/(x² + 1) = ⁴/₅

(h) (3x² + 7)/(x² + 4) = 2

(i) x² - 4x - 21 = 0

(j) 1/(x + 5) = (1/3) - 1/(x - 3)

(k) (3 - 2x)/(4 - 3x) = x

(l) $$\frac{5}{x}$$ - 2 = 2/x²

(m) (x + 1)/(x - 1) - (x - 1)/(x + 1) = ⁵/₆

(n) $$\frac{1}{x - 2}$$ + $$\frac{2}{x - 1}$$ = $$\frac{6}{x}$$

(o) (2x - 5)/(x - 3) - ²⁵/₃ = -2x/(x - 4)

(p) 4/(x + 4) - 1/(x + 1) = 2/(x + 2)

(q) 9x - 162/x - 63 = 0

(r) 15/(15 - x) = ³ˣ/₁₀

(s) x² - 7x - 60 = 0

(t) (4 - 3x) (2x + 3) = 5x

(u) (2x² + 2)/(x² - 2x) = ¹⁷/₄

(v) 14x + 5 - 3x² = 0

Answers for worksheet on quadratic equations are given below to check the exact answers of the above equations.

### Answers:

1. (a), (b), (d), (f)

2. (a) Yes

(b) No

(c) No

(d) No

(e) No

3. (a) -2, 4

(b) 4/3, 3

(c) 1, -2

(d) -1, -3/2

(e) -2/9, 4

(f) -1/5, 1/2

(g) -3, 3

(h) -1, 1

(i) -3, 7

(j) -3, 7

(k) 1

(l) 1/2, 2

(m) -1/5, 5

(n) 4/3, 3

(o) 6, 40/13

(p) 2, 39/8

(q) 9, -2

(r) 5, 10

(s) -5, 12

(t) 1, -2

(u) -2/9, 4

(v) 5, -1/3

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