Find the solutions of the quadratic equation 11x^(2)-6x-2=0. Choose 1 answer: (A) -(3)/(11)+-(sqrt31)/(11) (B) (3)/(11)+-(sqrt31)/(11)i (C) (3)/(11)+-(sqrt31)/(11) (D) (3)/(11)+-(sqrt52)/(11)i

Identify coefficients: Identify the coefficients of the quadratic equation. The quadratic equation is in the form ax^2 + bx + c = 0. For the equation 11x^2 - 6x - 2 = 0, the coefficients are: a = 11, b = -6, and c = -2.Use quadratic formula: Use the quadratic formula to find the solutions. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). We will substitute the values of a, b, and c into the formula.Calculate discriminant: Calculate the discriminant. The discriminant is the part of the quadratic formula under the square root: b^2 - 4ac. Let's calculate it: Discriminant = (-6)^2 - 4(11)(-2) = 36 + 88 = 124.Check discriminant: Check if the discriminant is positive, negative, or zero. Since the discriminant is 124, which is a positive number, we will have two real solutions.Calculate solutions: Calculate the solutions using the quadratic formula. x = (-(-6) ± √(124)) / (2 * 11) x = (6 ± √(124)) / 22 x = (6 ± 2√(31)) / 22 x = (3 ± √(31)) / 11Simplify solutions: Simplify the solutions. We can simplify the solutions by dividing both the numerator and the denominator by the greatest common divisor, which is already done in the previous step. So, the solutions are: x = (3 + √(31)) / 11 and x = (3 - √(31)) / 11

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Find the solutions of the quadratic equation
11x^(2)-6x-2=0.
Choose 1 answer:
(A)
-(3)/(11)+-(sqrt31)/(11)
(B)
(3)/(11)+-(sqrt31)/(11)i
(C)
(3)/(11)+-(sqrt31)/(11)
(D)
(3)/(11)+-(sqrt52)/(11)i

Find the solutions of the quadratic equation $11 x^{2}-6 x-2=0$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{3}{11} \pm \frac{\sqrt{31}}{11}$ $\newline$ (B) $\frac{3}{11} \pm \frac{\sqrt{31}}{11} i$ $\newline$ (C) $\frac{3}{11} \pm \frac{\sqrt{31}}{11}$ $\newline$ (D) $\frac{3}{11} \pm \frac{\sqrt{52}}{11} i$

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Q. Find the solutions of the quadratic equation

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

\newline

Choose

1

answer:

\newline

(A)

-\frac{3}{11} \pm \frac{\sqrt{31}}{11}

\newline

(B)

\frac{3}{11} \pm \frac{\sqrt{31}}{11} i

\newline

(C)

\frac{3}{11} \pm \frac{\sqrt{31}}{11}

\newline

(D)

\frac{3}{11} \pm \frac{\sqrt{52}}{11} i

Identify coefficients: Identify the coefficients of the quadratic equation. $\newline$ The quadratic equation is in the form $ax^2 + bx + c = 0$ . For the equation $11x^2 - 6x - 2 = 0$ , the coefficients are: $\newline$ $a = 11$ , $b = -6$ , and $c = -2$ .
Use quadratic formula: Use the quadratic formula to find the solutions. $\newline$ The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . We will substitute the values of $a$ , $b$ , and $c$ into the formula.
Calculate discriminant: Calculate the discriminant. $\newline$ The discriminant is the part of the quadratic formula under the square root: $b^2 - 4ac$ . Let's calculate it: $\newline$ Discriminant = $(-6)^2 - 4(11)(-2) = 36 + 88 = 124$ .
Check discriminant: Check if the discriminant is positive, negative, or zero. $\newline$ Since the discriminant is $124$ , which is a positive number, we will have two real solutions.
Calculate solutions: Calculate the solutions using the quadratic formula. $\newline$ $x = \frac{-(-6) \pm \sqrt{124}}{2 \cdot 11}$ $\newline$ $x = \frac{6 \pm \sqrt{124}}{22}$ $\newline$ $x = \frac{6 \pm 2\sqrt{31}}{22}$ $\newline$ $x = \frac{3 \pm \sqrt{31}}{11}$
Simplify solutions: Simplify the solutions. $\newline$ We can simplify the solutions by dividing both the numerator and the denominator by the greatest common divisor, which is already done in the previous step. So, the solutions are: $\newline$ x = $(3 + \sqrt{31}) / 11$ and x = $(3 - \sqrt{31}) / 11$