Chapter 9: Q. 9.51 (page 894)

Solve by using the Quadratic Formula: $\frac{1}{4} c^{2} - \frac{1}{3} c = \frac{1}{12}$

Short Answer

Expert verified

The solution of the quadratic equation is $c = \frac{2 \pm \sqrt{7}}{3}$

Step by step solution

Given information

We are given a quadratic equation $\frac{1}{4} c^{2} - \frac{1}{3} c = \frac{1}{12}$

We multiply by LCD and simplify

We get

$12 (\frac{1}{4} c^{2} - \frac{1}{3} c) = 12 \frac{1}{12} 3 c^{2} - 4 c = 1$

Subtract 1 from both sides and identify the values of a,b,c

We get,

$3 c^{2} - 4 c - 1 = 0$

On comparing with standard equation we get $a = 3, b = - 4, c = - 1$

Write quadratic formula and substitute the values

The quadratic formula can be given given as $c = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

On substituting the values we get

$c = \frac{4 \pm \sqrt{16 - 4 (3) (- 1)}}{2 (3)}$

Simplify

We get

$c = \frac{4 \pm \sqrt{16 + 12}}{6} c = \frac{4 \pm \sqrt{28}}{6} c = \frac{4 \pm 2 \sqrt{7}}{6}$

Take out and remove the common factor

We have,

$c = \frac{4 \pm 2 \sqrt{7}}{6} c = \frac{2 (2 \pm \sqrt{7})}{6} c = \frac{2 \pm \sqrt{7}}{6}$

Conclusion

The solution of the above quadratic equation is $c = \frac{2 \pm \sqrt{7}}{3}$

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Solve by using the Quadratic Formula: $\frac{1}{4} c^{2} - \frac{1}{3} c = \frac{1}{12}$

Short Answer

Step by step solution

Given information

We multiply by LCD and simplify

Subtract 1 from both sides and identify the values of a,b,c

Write quadratic formula and substitute the values

Simplify

Take out and remove the common factor

Conclusion

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Solve by using the Quadratic Formula:14c2-13c=112

Short Answer

Step by step solution

Given information

We multiply by LCD and simplify

Subtract 1 from both sides and identify the values of a,b,c

Write quadratic formula and substitute the values

Simplify

Take out and remove the common factor

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Geometry

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Calculus

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $\frac{1}{4} c^{2} - \frac{1}{3} c = \frac{1}{12}$