Question 1094145: For the quadratic equation 2x^2 + 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 by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
With the standard form of a quadratic equation
the discriminant
in the quadratic formula determines which of these different cases you have.
(1) If the discriminant is negative, there are no real solutions -- i.e., case A: two imaginary solutions.
(2) If the discriminant is zero, there is a single real solution: case B.
(3) If the discriminant is positive, then there are two real solutions. Furthermore, the solutions are rational if the discriminant is a perfect square (case C), or they are irrational if the discriminant is not a perfect square (case D).
With your quadratic, the discriminant is
So you have...
Case A, if b^2 is less than 24;
Case B, if b^2 is equal to 24;
Case C, if b^2-24 is a positive perfect square; and
Case D, if b^2-24 is positive but not a perfect square.
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