Question

Find the solutions to the following quadratic equation. −2x² 1x−1=0 select the correct answer below:

a. −1±7√i−4 1±7√i−4
b. −1±i−4 −1±3√i−2
c. −1±3√i−4
d. −1±7√i−2

Answer 1

The solutions to the quadratic equation −2x² + x − 1 = 0 are obtained using the quadratic formula, yielding x = -1 and x = −1/2 as the final answers.

The correct answer to the quadratic equation −2x² + x − 1 = 0 requires using the quadratic formula, which is -b ± √(b² - 4ac) over 2a. So in this case, with a = -2, b = 1, and c = -1, we substitute into the formula and calculate:

• −(-1) ± √(1² - 4(−2)(−1)) over 2(−2)
• 1 ± √(1 + 8) over −4
• 1 ± √9 over −4
• 1 ± 3 over −4

The final solutions are x = (1 + 3)/−4 and x = (1 - 3)/−4, simplified to x = -1 and x = −1/2.

So, the solutions are x = -1 and x = −1/2.