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Question

If m is slope of common tangents y = x2 - x + 1, y = x2 - 3x + 1 then m is

A
16
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B
7
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C
9
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D
-2
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Solution

The correct option is D -2
Let y = mx + c is common tangent
mx+c=x2x+1x2(1+4)x+1c=0mx+c=x23x+1x2(3+m)x+1c=0
Clearly Δ=0
(1+4)24(1c)=0m2+2m3+4c=0(3+m)24(1c)=0m2+6m+5+4c=0
On equality m2+4c value on both the equations
2m-3=6m+5
m=2

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