The equation x ( x - a) = 1 has two distinct solutions

acemi123

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The equation x ( x - a) = 1 has two distinct solutions


(A) if and only if -1 < a < 1
(B) for all a real
(C) for no real value of a
(D)ifandonlyif-2 < a< 2
(E) if and only if a > O

which statement is true?
 

MarkFL

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Hello, and welcome to FMH! :)

In order for a quadratic equation to have two distinct roots, what must be true of the discriminant?
 

acemi123

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Hello, and welcome to FMH! :)

In order for a quadratic equation to have two distinct roots, what must be true of the discriminant?
Yes, with discriminant it must be solved. The answer is ''for all real numbers'', but I wonder why? I need to be sure about it. Any explained suggest?
 

MarkFL

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In order to analyze the discriminant, we need to write the equation in standard form:

\(\displaystyle x^2-ax-1=0\)

What is the discriminant?
 

pka

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The answer is ''for all real numbers'', but I wonder why? . Any explained suggest?
Are there any real values of \(\displaystyle a\) for which \(\displaystyle a^2+4\) is negative?
 
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