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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 533 (page 988)

Solve the following quadratic equations. Use any method.
$\frac{9}{4} y^{2} - 3 y + 1 = 0$

Short Answer

Expert verified

The required solution is $y = \frac{2}{3}$ .

Step by step solution

01

Step 1. Given information.

We have:

$\frac{9}{4} y^{2} - 3 y + 1 = 0$

02

Step 2. Make a standard form of quadratic equation.

$\frac{9}{4} y^{2} - 3 y + 1 = 0$

Multiply both sides by $4 :$

$\frac{9}{4} y^{2} 路鈥� 4 - 3 y 路鈥� 4 + 1 路鈥� 4 = 0 路鈥� 4 9 y^{2} - 12 y + 4 = 0$

03

Step 3. Solve the quadratic equation.

For a quadratic equation of the standard form $a x^{2} + b x + c = 0$ , the solutions are:

$x_{1, 鈥� 2} = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

$For 鈥� a = 9, 鈥� b = - 12, 鈥� c = 4 y_{1, 鈥� 2} = \frac{- (- 12) 卤 \sqrt{{(- 12)}^{2} - 4 路鈥� 9 路鈥� 4}}{2 路鈥� 9} y_{1, 鈥� 2} = \frac{- (- 12) 卤 \sqrt{0}}{2 路鈥� 9} y = \frac{- (- 12)}{2 路鈥� 9} y = \frac{2}{3}$

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Most popular questions from this chapter

In the following exercises, solve by using the Quadratic Formula: $3 u^{2} + 7 u - 2 = 0$

Solve by using the Quadratic Formula: $4 a^{2} - 2 a + 8 = 0$

The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the length of the shadow and the length of the flag pole. Round to the nearest tenth.

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} m^{2} + \frac{1}{12} m = \frac{1}{4}$

Solve :- $x^{4} - 6 x^{2} + 8 = 0$

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