SOLUTION: Find the value of the discriminant and give the number of real solutions. 2x^2-5x=0

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Question 133370: Find the value of the discriminant and give the number of real solutions.
2x^2-5x=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

the discriminant consists of all of the terms in the square root. So the discriminant is

D=b%5E2-4ac

the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.


Now let's find the discriminant for y=2x%5E2-5x:

D=b%5E2-4ac Start with the given equation

D=%28-5%29%5E2-4%2A2%2A0 Plug in a=2, b=-5, c=0

D=25-4%2A2%2A0 Square -5 to get 25

D=25-0 Multiply -4*2*0 to get -0

D=25 Combine 25 and -0 to get 25


Since the discriminant equals 25 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.



Notice if we graph y=2x%5E2-5x, we get

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2-5x%29+

and we can see that there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.