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

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

Question 132421: Determine whether the following equations have a solution or not? Justify your answer
2x2 + x - 1 = 0

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
From the quadratic formula

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

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 :

Start with the given equation

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

Square 1 to get 1

Multiply -4*2*-1 to get 8

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 has two solutions.

Notice if we graph , we can see that there are two real solutions. So this verifies our answer.

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