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For which of the following values does ax^2 + 2x + c =0 not
[#permalink]
01 Apr 2007, 15:05
1
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For which of the following values does ax^2 + 2x + c =0 not have any real root?
A) ac>1
B) ac-1
E) it cannot be determined from the information given
I have an OA, so please provide your explanations!
A) ac>1
B) ac-1
E) it cannot be determined from the information given
I have an OA, so please provide your explanations!
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Re: For which of the following values does ax^2 + 2x + c =0 not
[#permalink]
01 Apr 2007, 15:22
(A) for me 
All is relying the study of b^2 - 4*a*c.... Actually, for the special case of b being an even, we can shortten this analysis by using the reduiced determinant : (b/2)^2 - a*c.
So, with b = 2, we have:
(b/2)^2 - a*c = 1 - a*c
If 1 - a*c < 0, there is no real root. Hence, a*c > 1.
All is relying the study of b^2 - 4*a*c.... Actually, for the special case of b being an even, we can shortten this analysis by using the reduiced determinant : (b/2)^2 - a*c.
So, with b = 2, we have:
(b/2)^2 - a*c = 1 - a*c
If 1 - a*c < 0, there is no real root. Hence, a*c > 1.
Re: For which of the following values does ax^2 + 2x + c =0 not
[#permalink]
01 Apr 2007, 16:36
for non real roots: (2^2-4ac) <0> ac>1