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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 10.55 (page 1185)

Solve the equation using quadratic formula.
$3 y^{2} - 5 y + 2 = 0$

Short Answer

Expert verified

The roots are $y = \frac{2}{3}, y = 1$ .

Step by step solution

01

Given Information.

The given equation is $3 y^{2} - 5 y + 2 = 0$ .

02

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

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

The equation is in standard form.

So,

$a = 3, b = - 5, c = 2$

03

Substitute the values in quadratic formula.

$y = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} y = \frac{- (- 5) 卤 \sqrt{(- 5)^{2} - 4 (3) (2)}}{2 (3)} y = \frac{5 卤 \sqrt{25 - 24}}{6} y = \frac{5 卤 \sqrt{1}}{6}$

04

Use square root property.

$y = \frac{5 卤 1}{6}$

Rewrite to show two solutions.

$y = \frac{5 + 1}{6} = \frac{6}{6} = 1 y = \frac{5 - 1}{6} = \frac{4}{6} = \frac{2}{3}$

Thus, the roots are $y = \frac{2}{3}, y = 1$ .

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Most popular questions from this chapter

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

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