SOLUTION: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary t      Log On


   

Question 234851: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
(3)^1/2y^2 -4y-7(3)^1/2=0
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
:
You have to know the rules of the discriminate
we are talking about the quadratic form y = ax^2 = bx + c
:
The discriminate formula
d = b^2 - 4 * a * c
If d is positive: two real roots
If d = 0: two equal and real roots
If d = less than 0, (neg) no real roots, (complex)
:
(3)^1/2y^2 -4y-7(3)^1/2=0
:
^1/2 = square root so we can write the equation:
sqrt%283%29y%5E2+-+4y+-+7sqrt%283%29 = 0
:
In this problem
a = sqrt%283%29
b = -4
c = -7sqrt%283%29
:
The discriminate
d = -4%5E2+-+4+%2A+sqrt%283%29+%2A+-7sqrt%283%29
we have a square root times a square root so we have
d = 16 - 4 * 3 * (-7)
d = 16 - (-84)
d = 16 + 84
d = 100, well positive, two real roots on this quad equation