Question

Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - x = -4 has.
a. two complex (nonreal) solutions
b. no real or complex solutions
c. one real solution
d. two real solutions

Answer 1

To determine the number and type of solutions, we need to calculate the discriminant of the quadratic equation 2x^2 - x = -4. The discriminant is given by the formula:

D = b^2 - 4ac

In this case, the equation is in the form ax^2 + bx + c = 0, where a = 2, b = -1, and c = 4. Substituting these values into the formula, we get:

D = (-1)^2 - 4(2)(-4)
D = 1 + 32
D = 33

The discriminant is positive (D > 0). When the discriminant is positive, the quadratic equation has two distinct real solutions. Therefore, the answer is:

d. two real solutions

Answer 2

wrong again!
D = D = (-1)^2 - 4(2)(4) = -31 < 0
so two complex roots

Answer 3

You're right, my apologies for the mistake. The correct calculation for the discriminant is:

D = (-1)^2 - 4(2)(-4) = 1 + 32 = 33

Since the discriminant is positive (D > 0), the quadratic equation 2x^2 - x = -4 has two distinct real solutions. The correct answer is:

d. two real solutions