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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 9: Q3. (page 600)

Use the Quadratic formula to find the exact solutions of the equation $2 x^{2} 鈭� 6 x + 3 = 0$ .
$A \frac{3 卤 \sqrt{3}}{2} B \frac{3 卤 \sqrt{2}}{4} C \frac{2 卤 \sqrt{5}}{3} D \frac{5 卤 \sqrt{2}}{2}$

Short Answer

Expert verified

The exact solutions $2 x^{2} 鈭� 6 x + 3 = 0$ are $\frac{3 卤 \sqrt{3}}{2}$ .

Step by step solution

01

Step 1. Identify.

Identify the coefficients of the equations by comparing the given equation $a x^{2} + b x + c = 0$ .

$a = 2, b = 鈭� 6$ and $c = 3$

02

Step 2. Write a quadratic formula.

A quadratic formula is $x = \frac{鈭� b 卤 \sqrt{b^{2} 鈭� 4 a c}}{2 a}$ .

03

Step 3. Substitute and simplify.

Substitute 2 for a, $- 6$ for b and 3 for c in $x = \frac{鈭� b 卤 \sqrt{b^{2} 鈭� 4 a c}}{2 a}$ .

$x = \frac{鈭� (鈭� 6) 卤 \sqrt{{(鈭� 6)}^{2} 鈭� 4 脳 2 脳 3}}{2 (2)} = \frac{12 卤 \sqrt{36 鈭� 24}}{4} = \frac{3 卤 \sqrt{3}}{2}$

Therefore, the exact solutions $2 x^{2} 鈭� 6 x + 3 = 0$ are $\frac{3 + \sqrt{3}}{2}$ and $\frac{3 鈭� \sqrt{3}}{2}$ . The obtained answer completely matches with option A, therefore option A is the required answer.

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Most popular questions from this chapter

Use a table of values to graph the given equation. State the domain and range.

$y = x^{2} + 3 x + 1$

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$16, 4, 鈭� 8, 鈭� 20, ...$

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$y^{2} 鈭� 8 y + 16 = 36$

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State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The expression $b^{2} 鈭� 4 a c$ is called the discriminant.

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