Question

Determine the number and type of solutions for the quadratic equation 3x² - 2x = 4.

a) Two real solutions
b) One real solution
c) Two complex solutions
d) No real solutions

Answer 1

The quadratic equation 3x² - 2x = 4 has two real solutions. Hence the correct answer is option A

Step-by-step explanation:

The quadratic equation 3x² - 2x = 4 can be solved by setting the equation equal to zero: 3x² - 2x - 4 = 0. To determine the number and type of solutions, we can use the discriminant, which is b² - 4ac. For this equation, a = 3, b = -2, and c = -4. The discriminant is (-2)² - 4(3)(-4) = 4 + 48 = 52.

Since the discriminant is positive, the equation has two real solutions. Therefore, the answer is option a) Two real solutions.