QuestionJuly 14, 2025

Solve the quadratic equation by using the quadratic formula. 3x^2+4x+2=0 x=square (Use a comma to separate answers as needed. Round to the nearest hundredth as needed. Express complex numbers in terms of i.)

Solve the quadratic equation by using the quadratic formula. 3x^2+4x+2=0 x=square (Use a comma to separate answers as needed. Round to the nearest hundredth as needed. Express complex numbers in terms of i.)
Solve the quadratic equation by using the quadratic formula. 3x^2+4x+2=0 x=square (Use a comma to separate answers as needed. Round to the nearest hundredth as needed. Express complex numbers in terms of i.)

Solution
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Answer

x = \frac{-2 + i\sqrt{2}}{3}, \frac{-2 - i\sqrt{2}}{3} Explanation 1. Identify coefficients Coefficients are a = 3, b = 4, c = 2. 2. Apply quadratic formula Use the formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. 3. Calculate discriminant Discriminant is b^2 - 4ac = 4^2 - 4 \cdot 3 \cdot 2 = 16 - 24 = -8. 4. Compute roots using complex numbers Since the discriminant is negative, use i for imaginary part: x = \frac{-4 \pm \sqrt{-8}}{6} = \frac{-4 \pm 2i\sqrt{2}}{6}. 5. Simplify expression Simplify to x = \frac{-2 \pm i\sqrt{2}}{3}.

Explanation

1. Identify coefficients<br /> Coefficients are $a = 3$, $b = 4$, $c = 2$.<br />2. Apply quadratic formula<br /> Use the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.<br />3. Calculate discriminant<br /> Discriminant is $b^2 - 4ac = 4^2 - 4 \cdot 3 \cdot 2 = 16 - 24 = -8$.<br />4. Compute roots using complex numbers<br /> Since the discriminant is negative, use $i$ for imaginary part: $x = \frac{-4 \pm \sqrt{-8}}{6} = \frac{-4 \pm 2i\sqrt{2}}{6}$.<br />5. Simplify expression<br /> Simplify to $x = \frac{-2 \pm i\sqrt{2}}{3}$.
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