Solve Quadratic and rational Equations

Solve a set of questions related to quadratic and rational equations. A set of 10 questions are included and have detailed solutions.

You may prefer to go through a tutorial on Equations with Rational Expressions before you start solving the following equations.

Questions with Solutions

Question 1

Find all real solution to the quadratic equation
x2 + 2 x = - 1

Detailed Solution.

Question 2

Find all real solution to the quadratic equation
x2 + 2 = x + 5

Detailed Solution.

Question 3

Find all real solution to the equation

- ( x + 2)(x - 1) = 3

Detailed Solution.

Question 4

Find all real solution to the rational equation.
(2x + 1) / (x + 2) = x - 1



Detailed Solution.

Question 5

Find all real solution to the rational equation.
2 / (x + 1) - 1 / (x - 2) = -1

Detailed Solution.

Question 6

Find all real solution to the equation.
2(x - 2)2 - 6 = -2

Detailed Solution.

Question 7

Find all real solution to the rational equation.
x / (x + 4) = -3 / (x - 2) + 18 / (x - 2) (x + 4)

Detailed Solution.

Question 8

Find all real solution to the quadratic equation.
x2 - 3(x - 3)2 = 2

Detailed Solution.

Question 9

Find all real solution to the rational equation.

1 / (x - 4) + 1 / (x + 4)= x2 / (x2 - 16)

Detailed Solution.

Question 10

Find all real solution to the rational equation.

-x / (x + 3) - x / (x - 3) = - 4 / (x2 - 9) - 1 / (x + 3)

Detailed Solution.



More references and links to tutorials and problems on equations

Solve Quadratic Equations Using Discriminants.
Tutorial on Equations of the Quadratic Form.
Math Problems, Questions and Online Self Tests.
More Intermediate and College Algebra Questions and Problems with Answers.