Chapter 10: Q 127 (page 1195)

Solve the equation using quadratic formula.
$\frac{3}{4} b^{2} + \frac{1}{2} b = \frac{3}{8}$

Short Answer

Expert verified

The roots are $b = \frac{- 2 + \sqrt{22}}{6}, b = \frac{- 2 - \sqrt{22}}{6}$ .

Step by step solution

Given Information.

The given equation is $\frac{3}{4} b^{2} + \frac{1}{2} b = \frac{3}{8}$ .

Write the quadratic equation in standard form and identify a,b,c.

$\frac{3}{4} b^{2} + \frac{1}{2} b - \frac{3}{8} = 0$

Here,

$a = \frac{3}{4}, b = \frac{1}{2}, c = - \frac{3}{8}$

Substitute the values in quadratic formula.

$b = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} b = \frac{- \frac{1}{2} \pm \sqrt{{(\frac{1}{2})}^{2} - 4 (\frac{3}{4}) (- \frac{3}{8})}}{2 (\frac{3}{4})} b = \frac{- \frac{1}{2} \pm \sqrt{\frac{1}{4} + \frac{36}{32}}}{\frac{3}{2}} b = \frac{- \frac{1}{2} \pm \sqrt{\frac{44}{32}}}{\frac{3}{2}} b = \frac{- \frac{1}{2} \pm \sqrt{\frac{22}{16}}}{\frac{3}{2}}$

Use square root property.

$b = \frac{- \frac{1}{2} \pm \frac{\sqrt{22}}{4}}{\frac{3}{2}}$

Simplify.

$b = \frac{\frac{1}{2} (- 1 \pm \frac{\sqrt{22}}{2})}{\frac{3}{2}} b = \frac{- 1 \pm \frac{\sqrt{22}}{2}}{3} b = \frac{- 2 \pm \sqrt{22}}{6}$

Rewrite to show two solutions.

$b = \frac{- 2 + \sqrt{22}}{6}, b = \frac{- 2 - \sqrt{22}}{6}$ .

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Solve the equation using quadratic formula.
$\frac{3}{4} b^{2} + \frac{1}{2} b = \frac{3}{8}$

Short Answer

Step by step solution

Given Information.

Write the quadratic equation in standard form and identify a,b,c.

Substitute the values in quadratic formula.

Use square root property.

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Solve the equation using quadratic formula. 34b2+12b=38

Short Answer

Step by step solution

Given Information.

Write the quadratic equation in standard form and identify a,b,c.

Substitute the values in quadratic formula.

Use square root property.

One App. One Place for Learning.

Most popular questions from this chapter

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Solve the equation using quadratic formula.
$\frac{3}{4} b^{2} + \frac{1}{2} b = \frac{3}{8}$