Find the solutions of the quadratic equation 2x^(2)-8x-9=0. Choose 1 answer: (A) 2+-(sqrt34)/(2)i (B) -2+-(sqrt34)/(2)i (C) 2+-(sqrt34)/(2) (D) 1+-(sqrt34)/(4)

Identify coefficients: Identify the coefficients of the quadratic equation 2x^2 - 8x - 9 = 0. The standard form of a quadratic equation is ax^2 + bx + c = 0. Here, a = 2, b = -8, and c = -9.Use quadratic formula: Use the quadratic formula to solve for x. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a).Calculate discriminant: Calculate the discriminant D = b^2 - 4ac. D = (-8)^2 - 4(2)(-9) D = 64 + 72 D = 136 The discriminant is positive, which means there are two real and distinct solutions.Substitute values into formula: Substitute the values of a, b, and D into the quadratic formula. x = (-(-8) ± sqrt(136)) / (2 * 2) x = (8 ± sqrt(136)) / 4Simplify square root: Simplify the square root of the discriminant. sqrt(136) can be simplified to sqrt(4 * 34), which is 2 * sqrt(34).Substitute simplified square root: Substitute the simplified square root back into the equation. x = (8 ± 2 * sqrt(34)) / 4Simplify equation: Simplify the equation by dividing both terms in the numerator by 4. x = (8 / 4) ± (2 * sqrt(34) / 4) x = 2 ± (sqrt(34) / 2)Write final solutions: Write the final solutions. The solutions are x = 2 + (sqrt(34) / 2) and x = 2 - (sqrt(34) / 2).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the solutions of the quadratic equation
2x^(2)-8x-9=0.
Choose 1 answer:
(A)
2+-(sqrt34)/(2)i
(B)
-2+-(sqrt34)/(2)i
(C)
2+-(sqrt34)/(2)
(D)
1+-(sqrt34)/(4)

Find the solutions of the quadratic equation $2 x^{2}-8 x-9=0$ . $\newline$ Choose $1$ answer: $\newline$ (A) $2 \pm \frac{\sqrt{34}}{2} i$ $\newline$ (B) $-2 \pm \frac{\sqrt{34}}{2} i$ $\newline$ (C) $2 \pm \frac{\sqrt{34}}{2}$ $\newline$ (D) $1 \pm \frac{\sqrt{34}}{4}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve polynomial equations

Full solution

Q. Find the solutions of the quadratic equation

2 x^{2}-8 x-9=0

\newline

Choose

1

answer:

\newline

(A)

2 \pm \frac{\sqrt{34}}{2} i

\newline

(B)

-2 \pm \frac{\sqrt{34}}{2} i

\newline

(C)

2 \pm \frac{\sqrt{34}}{2}

\newline

(D)

1 \pm \frac{\sqrt{34}}{4}

Identify coefficients: Identify the coefficients of the quadratic equation $2x^2 - 8x - 9 = 0$ . $\newline$ The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . Here, $a = 2$ , $b = -8$ , and $c = -9$ .
Use quadratic formula: Use the quadratic formula to solve for x. The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ .
Calculate discriminant: Calculate the discriminant $D = b^2 - 4ac$ . $\newline$ $D = (-8)^2 - 4(2)(-9)$ $\newline$ $D = 64 + 72$ $\newline$ $D = 136$ $\newline$ The discriminant is positive, which means there are two real and distinct solutions.
Substitute values into formula: Substitute the values of $a$ , $b$ , and $D$ into the quadratic formula. $\newline$ $x = \frac{-(-8) \pm \sqrt{136}}{2 \cdot 2}$ $\newline$ $x = \frac{8 \pm \sqrt{136}}{4}$
Simplify square root: Simplify the square root of the discriminant. $\sqrt{136}$ can be simplified to $\sqrt{4 \times 34}$ , which is $2 \times \sqrt{34}$ .
Substitute simplified square root: Substitute the simplified square root back into the equation. $x = \frac{8 \pm 2 \cdot \sqrt{34}}{4}$
Simplify equation: Simplify the equation by dividing both terms in the numerator by $4$ . $\newline$ $x = \frac{8}{4} \pm \frac{2 \cdot \sqrt{34}}{4}$ $\newline$ $x = 2 \pm \frac{\sqrt{34}}{2}$
Write final solutions: Write the final solutions. $\newline$ The solutions are $x = 2 + \left(\frac{\sqrt{34}}{2}\right)$ and $x = 2 - \left(\frac{\sqrt{34}}{2}\right)$ .