Question

question 20 of 40
jonathan must determine the solutions of the quadratic equation
0 = 2x² + x + 4.
which of the following is a solution to the equation?

a. \\(\frac{-1 - isqrt{23}}{2}\\)

b. \\(\frac{-1 + isqrt{10}}{4}\\)

c. \\(\frac{-1 - isqrt{31}}{4}\\)

d. \\(\frac{-1 - 3i}{2}\\)

Explanation:

Step1: Identify quadratic coefficients

For \(2x^2 + x + 4 = 0\), \(a=2\), \(b=1\), \(c=4\).

Step2: Calculate discriminant

Discriminant \(D = b^2 - 4ac = 1^2 - 4(2)(4) = 1 - 32 = -31\).

Step3: Apply quadratic formula

Quadratic formula: \(x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-1 \pm i\sqrt{31}}{4}\).

Answer:

C. \(\frac{-1-i\sqrt{31}}{4}\)