Find the solutions of the quadratic equation -3x^(2)+4x+1=0. Choose 1 answer: (A) (2)/(6)∓(sqrt7)/(6) (B) (2)/(6)∓(sqrt7)/(6)i (c) (2)/(3)∓(sqrt7)/(3)i (D) (2)/(3)∓(sqrt7)/(3)

Quadratic Formula: To find the solutions of the quadratic equation -3x^(2)+4x+1=0, we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a, b, and c are the coefficients of the terms in the quadratic equation ax^2 + bx + c = 0. In this case, a = -3, b = 4, and c = 1.Calculating the Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. Discriminant = (4)^2 - 4*(-3)*(1) = 16 + 12 = 28.Determining the Number of Solutions: Since the discriminant is positive, we will have two real solutions. Now we can apply the quadratic formula: x = [-4 ± sqrt(28)] / (2*(-3)).Applying the Quadratic Formula: We simplify the square root of 28 by factoring it into 4*7 and taking the square root of 4 out of the square root sign: sqrt(28) = sqrt(4*7) = 2*sqrt(7).Simplifying the Square Root: Now we substitute the simplified square root back into the quadratic formula: x = [-4 ± 2*sqrt(7)] / (-6).Substituting the Simplified Square Root: We can simplify the fraction by dividing both the numerator and the denominator by 2: x = [-2 ± sqrt(7)] / (-3).Simplifying the Fraction: Finally, we can write the solutions as two separate numbers: x = (-2)/(3) + (sqrt(7))/(3) or x = (-2)/(3) - (sqrt(7))/(3).

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Find the solutions of the quadratic equation
-3x^(2)+4x+1=0.
Choose 1 answer:
(A)
(2)/(6)∓(sqrt7)/(6)
(B)
(2)/(6)∓(sqrt7)/(6)i
(c)
(2)/(3)∓(sqrt7)/(3)i
(D)
(2)/(3)∓(sqrt7)/(3)

Find the solutions of the quadratic equation $-3 x^{2}+4 x+1=0$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2}{6} \mp \frac{\sqrt{7}}{6}$ $\newline$ (B) $\frac{2}{6} \mp \frac{\sqrt{7}}{6} i$ $\newline$ (C) $\frac{2}{3} \mp \frac{\sqrt{7}}{3} i$ $\newline$ (D) $\frac{2}{3} \mp \frac{\sqrt{7}}{3}$

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Q. Find the solutions of the quadratic equation

-3 x^{2}+4 x+1=0

\newline

Choose

1

answer:

\newline

(A)

\frac{2}{6} \mp \frac{\sqrt{7}}{6}

\newline

(B)

\frac{2}{6} \mp \frac{\sqrt{7}}{6} i

\newline

(C)

\frac{2}{3} \mp \frac{\sqrt{7}}{3} i

\newline

(D)

\frac{2}{3} \mp \frac{\sqrt{7}}{3}

Quadratic Formula: To find the solutions of the quadratic equation $-3x^{2}+4x+1=0$ , we can use the quadratic formula, which is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ , where $a$ , $b$ , and $c$ are the coefficients of the terms in the quadratic equation $ax^2 + bx + c = 0$ . $\newline$ In this case, $a = -3$ , $b = 4$ , and $c = 1$ .
Calculating the Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . $\newline$ Discriminant = $(4)^2 - 4(-3)(1) = 16 + 12 = 28$ .
Determining the Number of Solutions: Since the discriminant is positive, we will have two real solutions. $\newline$ Now we can apply the quadratic formula: $\newline$ $x = \frac{{-4 \pm \sqrt{28}}}{{2 \cdot (-3)}}$ .
Applying the Quadratic Formula: We simplify the square root of $28$ by factoring it into $4 \times 7$ and taking the square root of $4$ out of the square root sign: $\sqrt{28} = \sqrt{4 \times 7} = 2 \times \sqrt{7}$ .
Simplifying the Square Root: Now we substitute the simplified square root back into the quadratic formula: $\newline$ $x = \frac{{-4 \pm 2\sqrt{7}}}{{-6}}$ .
Substituting the Simplified Square Root: We can simplify the fraction by dividing both the numerator and the denominator by $2$ : $\newline$ $x = \frac{{-2 \pm \sqrt{7}}}{{-3}}$ .
Simplifying the Fraction: Finally, we can write the solutions as two separate numbers: $\newline$ x = $\frac{-2}{3} + \frac{\sqrt{7}}{3}$ or x = $\frac{-2}{3} - \frac{\sqrt{7}}{3}$ .