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

#### acemi123

##### New member
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

##### Super Moderator
Staff member
Hello, and welcome to FMH! In order for a quadratic equation to have two distinct roots, what must be true of the discriminant?

• topsquark

#### acemi123

##### New member
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

##### Super Moderator
Staff member
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?

• acemi123 and topsquark

#### pka

##### Elite Member
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?

• topsquark and acemi123