Chapter 9: Q3. (page 600)

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

Short Answer

Expert verified

The exact solutions $2 x^{2} - 6 x + 3 = 0$ are $\frac{3 \pm \sqrt{3}}{2}$ .

Step by step solution

Step 1. Identify.

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

$a = 2, b = - 6$ and $c = 3$

Step 2. Write a quadratic formula.

A quadratic formula is $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

Step 3. Substitute and simplify.

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

$x = \frac{- (- 6) \pm \sqrt{{(- 6)}^{2} - 4 \times 2 \times 3}}{2 (2)} = \frac{12 \pm \sqrt{36 - 24}}{4} = \frac{3 \pm \sqrt{3}}{2}$

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

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

Short Answer

Step by step solution

Step 1. Identify.

Step 2. Write a quadratic formula.

Step 3. Substitute and simplify.

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Use the Quadratic formula to find the exact solutions of the equation 2x2−6x+3=0.A3±32B3±24C2±53D5±22

Short Answer

Step by step solution

Step 1. Identify.

Step 2. Write a quadratic formula.

Step 3. Substitute and simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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