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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (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


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ax%5E2%2B5%2Ax-1=0 ( notice a=2, b=5, and c=-1)





x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29 Plug in a=2, b=5, and c=-1




x+=+%28-5+%2B-+sqrt%28+25-4%2A2%2A-1+%29%29%2F%282%2A2%29 Square 5 to get 25




x+=+%28-5+%2B-+sqrt%28+25%2B8+%29%29%2F%282%2A2%29 Multiply -4%2A-1%2A2 to get 8




x+=+%28-5+%2B-+sqrt%28+33+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+sqrt%2833%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-5+%2B-+sqrt%2833%29%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%28-5+%2B+sqrt%2833%29%29%2F4 or x+=+%28-5+-+sqrt%2833%29%29%2F4



Now break up the fraction



x=-5%2F4%2Bsqrt%2833%29%2F4 or x=-5%2F4-sqrt%2833%29%2F4



Simplify



x=-5%2F4%2Bsqrt%2833%29%2F4 or x=-5%2F4-sqrt%2833%29%2F4



So the solutions are:

x=-5%2F4%2Bsqrt%2833%29%2F4 or x=-5%2F4-sqrt%2833%29%2F4

Answer by stanbon(75887) About Me  (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.
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Note: sqrt(33) is irrational.
Since the discriminant is positive, and sqrt(33) is
irrational, the equation has 2 real, irrational roots.
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Cheers,
Stan H.
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