Find the solutions of the quadratic equation 2x^(2)+6x-2=0. Choose 1 answer: (A) -(3)/(4)+-(sqrt13)/(4) (B) (3)/(2)+-(sqrt13)/(2) (c) -(3)/(2)+-(sqrt13)/(2) (D) -(3)/(2)+-(sqrt13)/(2)i

Quadratic Formula: We will use the quadratic formula to solve the equation 2x^2 + 6x - 2 = 0. The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.Identifying Coefficients: First, identify the coefficients a, b, and c from the quadratic equation. In our equation, a = 2, b = 6, and c = -2.Calculating the Discriminant: Next, calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. For our equation, the discriminant is 6^2 - 4(2)(-2) = 36 + 16 = 52.Plugging Values into the Formula: Now, plug the values of a, b, and the discriminant into the quadratic formula to find the solutions for x. We have x = (-6 ± √52) / (4). Simplify √52 to √(4*13) = 2√13.Simplifying the Formula: Substitute √52 with 2√13 in the formula to get x = (-6 ± 2√13) / (4). Now, we can simplify this by dividing both terms in the numerator by 2.Final Solutions: After simplifying, we get x = (-3 ± √13) / (2). These are the solutions to the quadratic equation.

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Find the solutions of the quadratic equation
2x^(2)+6x-2=0.
Choose 1 answer:
(A)
-(3)/(4)+-(sqrt13)/(4)
(B)
(3)/(2)+-(sqrt13)/(2)
(c)
-(3)/(2)+-(sqrt13)/(2)
(D)
-(3)/(2)+-(sqrt13)/(2)i

Find the solutions of the quadratic equation $2 x^{2}+6 x-2=0$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{3}{4} \pm \frac{\sqrt{13}}{4}$ $\newline$ (B) $\frac{3}{2} \pm \frac{\sqrt{13}}{2}$ $\newline$ (C) $-\frac{3}{2} \pm \frac{\sqrt{13}}{2}$ $\newline$ (D) $-\frac{3}{2} \pm \frac{\sqrt{13}}{2} i$

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Q. Find the solutions of the quadratic equation

2 x^{2}+6 x-2=0

\newline

Choose

1

answer:

\newline

(A)

-\frac{3}{4} \pm \frac{\sqrt{13}}{4}

\newline

(B)

\frac{3}{2} \pm \frac{\sqrt{13}}{2}

\newline

(C)

-\frac{3}{2} \pm \frac{\sqrt{13}}{2}

\newline

(D)

-\frac{3}{2} \pm \frac{\sqrt{13}}{2} i

Quadratic Formula: We will use the quadratic formula to solve the equation $2x^2 + 6x - 2 = 0$ . The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$ .
Identifying Coefficients: First, identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation. In our equation, $a = 2$ , $b = 6$ , and $c = -2$ .
Calculating the Discriminant: Next, calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . For our equation, the discriminant is $6^2 - 4(2)(-2) = 36 + 16 = 52$ .
Plugging Values into the Formula: Now, plug the values of $a$ , $b$ , and the discriminant into the quadratic formula to find the solutions for $x$ . We have $x = \frac{{-6 \pm \sqrt{52}}}{{4}}$ . Simplify $\sqrt{52}$ to $\sqrt{4 \cdot 13} = 2\sqrt{13}$ .
Simplifying the Formula: Substitute $\sqrt{52}$ with $2\sqrt{13}$ in the formula to get $x = \frac{-6 \pm 2\sqrt{13}}{4}$ . Now, we can simplify this by dividing both terms in the numerator by $2$ .
Final Solutions: After simplifying, we get $x = \frac{{-3 \pm \sqrt{13}}}{{2}}$ . These are the solutions to the quadratic equation.