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High School Math : Simplifying and Expanding Quadratic Equations

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Example Questions

Example Question #1 : Understanding Quadratic Equations

Solve the following equation using the quadratic form:

x^4-9=0

Possible Answers:

$x=\pm\sqrt{6}, \pm i\sqrt{6}$

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

$x=\pm\sqrt{5}, \pm i\sqrt{5}$

$x=\pm\sqrt{4}, \pm i\sqrt{4}$

$x=\pm\sqrt{2}, \pm i\sqrt{2}$

Correct answer:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Explanation:

Factor the equation and solve:

x^4-9=0

(x^2-3)(x^2+3)=0

x^2 = 3

$x = \pm \sqrt{3}$

x^2 = -3

$x = \pm i\sqrt{3}$

Therefore there are four answers:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

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Example Question #32 : Intermediate Single Variable Algebra

Solve the following equation using the quadratic form:

$x-4\sqrt{x}-45=0$

Possible Answers:

x=81

x=36

x=49

x=64

x=25

Correct answer:

x=81

Explanation:

Factor the equation and solve:

$x-4\sqrt{x}-45=0$

$(\sqrt{x}-9)(\sqrt{x}+5)=0$

$\sqrt{x}=9$

x=81

$\sqrt{x}=-5$

This has no solutions.

Therefore there is only one answer:

x=81

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High School Math : Simplifying and Expanding Quadratic Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Understanding Quadratic Equations

Example Question #32 : Intermediate Single Variable Algebra

All High School Math Resources

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