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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. 127 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$3 y^{2} + 5 y - 2 = 0$

Short Answer

Expert verified

The solutions of the given equation are $y = \frac{1}{3}$ and $y = - 2$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$3 y^{2} + 5 y - 2 = 0$

02

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a x^{2} + b x + c = 0$ is:

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

In the given equation, $a = 3, b = 5, c = - 2$ . Substitute these values in Quadratic Formula.

$y = \frac{- 5 卤 \sqrt{5^{2} - 4 (3) (- 2)}}{2 (3)}$

03

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} y & = & \frac{- 5 卤 \sqrt{25 + 24}}{6} \\ y & = & \frac{- 5 卤 \sqrt{49}}{6} \\ y & = & \frac{- 5 卤 7}{6} \end{array}$

Now,

$\begin{array}{rcl} y & = & \frac{- 5 + 7}{6} \\ y & = & \frac{2}{6} \\ y & = & \frac{1}{3} \end{array}$

And,

$\begin{array}{rcl} y & = & \frac{- 5 - 7}{6} \\ y & = & \frac{- 12}{6} \\ y & = & - 2 \end{array}$

04

Step 4. Conclusion.

The solutions of the given equation are $y = \frac{1}{3}$ and $y = - 2$ .

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