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Question

Compute set of values of a such that y=x2x1ax(x ϵ R) attains all real values, is

A
[1,4]
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B
(0,4]
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C
(0,1]
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D
[1,)
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Solution

The correct option is D [1,)
y=x2x1axyaxy=x2xx2+x(ay1)y=0
Then, x=(1ay)±(ay1)2+4y2
for all real value of x,y.
(ay1)2+4y0.
a2y2+4y2ay+10
for above equation,
(42a)24a201616a0( for real y)
a1
a[1,)
option D is correct

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