SOLUTION: The value of the discriminant for the equation below is 33. 2x^2+5x-1=0 What does the value of the discriminant mean for this equation? A. The equation has 1 real, rational

Question 827288: The value of the discriminant for the equation below is 33.
2x^2+5x-1=0
What does the value of the discriminant mean for this equation?

A. The equation has 1 real, rational root.
B. The equation has 2 real, rational roots.
C. The equation has 1 real, irrational root.
D. The equation has 2 real, irrational roots.
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
B. The equation has 2 real, rational roots.
irrational roots always come in pairs so and c cannot be
it is positive so there is a rational root

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=5, and c=-1

Square 5 to get 25

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The value of the discriminant for the equation below is 33.
2x^2+5x-1=0
What does the value of the discriminant mean for this equ ation?
A. The equation has 1 real, rational root.
B. The equation has 2 real, rational roots.
C. The equation has 1 real, irrational root.
D. The equation has 2 real, irrational roots.
-----
Note: sqrt(33) is irrational.
Since the discriminant is positive, and sqrt(33) is
irrational, the equation has 2 real, irrational roots.
============
Cheers,
Stan H.
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