SOLUTION: Determine whether the following equations have a solution or not? Justify your answer 2x2 + x - 1 = 0

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Question 132421: Determine whether the following equations have a solution or not? Justify your answer
2x2 + x - 1 = 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%2Bx-1:

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

D=%281%29%5E2-4%2A2%2A-1 Plug in a=2, b=1, c=-1

D=1-4%2A2%2A-1 Square 1 to get 1

D=1%2B8 Multiply -4*2*-1 to get 8

D=9 Combine 1 and 8 to get 9


Since the discriminant equals 9 (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.



So the quadratic y=2x%5E2%2Bx-1 has two solutions.



Notice if we graph y=2x%5E2%2Bx-1, we can see that there are two real solutions. So this verifies our answer.


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2%2Bx-1%29+