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If x2 - tx + t = 0, where t > 0, has one solution for x, then x is equal to
A) 1
B) - 1
C) - t + t2- t
D) 2
E) - t
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We are given the equation x^2 - tx + t = 0, where t > 0,
and the problem asks to find its root x under the condition that this root is UNIQUE,
which means that there is no other roots.
It is the case, when a quadratic equation has MERGING roots.
For it, the necessary and sufficient condition is d = 0, where " d " is the discriminant
of the quadratic equation d = (b^2 - 4ac).
In our case, b = -t, a = 1, c = t, so the discriminant is d = (-t)^2 - 4t = t^2 - 4t.
The discriminant is zero, t^2-4t = 0 = t*(t-4), if "t" is 0 or 4.
The case t= 0 is excluded by the condition, since t must be positive.
So, t = 4 is the only possibility.
For t = 4 we have
x^2 -4t + 4 = (x-2)^2,
and the only root of it is x = 2.
ANSWER. Under given conditions, x = 2.
Solved.