SOLUTION: For the quadratic equation {{{ 2x^2+2x+3=0 }}}, explain how to find a value of "b" where the discriminant yields a quadratic equation with the following types of solutions. a. t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: For the quadratic equation {{{ 2x^2+2x+3=0 }}}, explain how to find a value of "b" where the discriminant yields a quadratic equation with the following types of solutions. a. t      Log On


   

Question 530526: For the quadratic equation +2x%5E2%2B2x%2B3=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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is +b%5E2+-+4%2Aa%2Ac+
where +y+=+ax%5E2+%2B+bx+%2B+c+
In the quadratic formula, it appears
under the square root sign
(1)
2 imaginary solutions:
+b%5E2+%3C+4%2Aa%2Ac+
(2)
1 real solution:
+b%5E2+=+4%2Aa%2Ac+
(3)
2 rational solutions:
+b%5E2+%3E+4%2Aa%2Ac+
and
+b%5E2+-+4%2Aa%2Ac+ is a perfect square
(4)
+b%5E2+%3E+4%2Aa%2Ac+
and
+b%5E2+-+4%2Aa%2Ac+ is not a perfect square