Question

Find the solutions to the quadratic equation 2x2−8x−9=0.

A. x=3
B. x=−1/2
C. x=4+√34/2
D. x=4-√34/2
E. x=5

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf 2x^2 - 8x - 9 = 0$}`

`\Large \text{$ \sf a = 2$}`

`\Large \text{$ \sf b = -8$}`

`\Large \text{$ \sf c = -9$}`

`\Large \text{$ \sf \Delta = b^2 - 4.a.c$}`

`\Large \text{$ \sf \Delta = (-8)^2 - 4.2.(-9)$}`

`\Large \text{$ \sf \Delta = 64 + 72$}`

`\Large \text{$ \sf \Delta = 136$}`

`\Large \text{$ \sf x = (-b \pm √(\Delta))/(2a) = (8 \pm √(136))/(4) \rightarrow \begin{cases}\sf{x' = (4 + √(34))/(2)}\\\\\sf{x'' = (4 - √(34))/(2)}\end{cases}$}`

`\Large \text{$ \sf S = \left\{(4 + √(34))/(2),\:(4 - √(34))/(2)\right\}$}`

Answer 2

The solutions to the quadratic equation 2x^2 - 8x - 9 = 0 are found using the quadratic formula. By substituting the coefficients into the formula, we get two solutions which correspond to x = (2 + √34/2) and x = (2 - √34/2).

Step-by-step explanation:

To find the solutions to the quadratic equation 2x2 - 8x - 9 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation of the form ax2 + bx + c = 0.

In our case, a = 2, b = -8, and c = -9. Applying these values to the quadratic formula, we get:

x = (-(-8) ± √((-8)2 - 4 * 2 * -9)) / (2 * 2)

x = (8 ± √(64 + 72)) / 4

x = (8 ± √136) / 4

x = (8 ± 2√34) / 4

Now we simplify to get the two solutions:

1. x = (8 + 2√34) / 4 = 2 + √34/2
2. x = (8 - 2√34) / 4 = 2 - √34/2

These solutions correspond to the choices C and D in the original question.