Chapter 10: Q 279 (page 1236)

Solve the quadratic equation by quadratic formula . $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

Short Answer

Expert verified

The required result is $p = \frac{4 - \sqrt{6}}{5}, \frac{4 + \sqrt{6}}{5}$

Step by step solution

Given Information

The given equation is $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

Simplify the expression `to write in standard form

Take LCM

\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20} \frac{5 p^{2} - 8 p}{40} = - \frac{1}{20}

$\frac{5 p^{2} - 8 p}{2} = - \frac{1}{1} 5 p^{2} - 8 p = - 2$

$5 p^{2} - 8 p + 2 = 0$

After converting in standard form .Identify the value of a,b,c

$a = 5, b = - 8, c = 2$

Substitute the values in quadratic formula.

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} p = \frac{- (- 8) \pm \sqrt{{(- 8)}^{2} - 4 (5) (2)}}{2 (5)} p = \frac{8 \pm \sqrt{64 - 40}}{10} p = \frac{8 \pm \sqrt{24}}{10} p = \frac{8 \pm 2 \sqrt{6}}{10} p = \frac{4 \pm \sqrt{6}}{5} p = \frac{4 - \sqrt{6}}{5}, \frac{4 + \sqrt{6}}{5}$

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Solve the quadratic equation by quadratic formula . $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

Short Answer

Step by step solution

Given Information

Simplify the expression `to write in standard form

After converting in standard form .Identify the value of a,b,c

Substitute the values in quadratic formula.

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Solve the quadratic equation by quadratic formula .18p2-15p=-120

Short Answer

Step by step solution

Given Information

Simplify the expression `to write in standard form

After converting in standard form .Identify the value of a,b,c

Substitute the values in quadratic formula.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Solve the quadratic equation by quadratic formula . $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$