For the quadratic equation 2x^2 + bx + 3 = 0, explain how to find a value where the discriminat yields a quadratic equation with the following types of solutions.

Question

Quadratic equations can have several types of solutions. For a quadratic equation in standard form, ax² + bx + c = 0, the expression b² - 4ac (known as the discriminant), can quickly give some insight into the nature of solution (s).

For the quadratic equation 2x² + bx + 3 = 0, explain how to find a value of b where the discriminant yields a quadratic equation with the following types of solutions.

a. two imaginary solutions b. one real solution

c. two rational solutions d. two irrational solutions

Answer 1

a. b² - 4(2)(3) < 0

b. b² - 4(2)(3) = 0

c. b² - 4(2)(3) > 0

d. b² - 4(2)(3) > 0

Answer 2