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Question

If the LCM of (x2+3x)(x2+3x+2) and (x2+6x+8)(x2+kx+6) is x(x+1)(x+2)2(x+3)(x+4) then find k.

A
2
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B
3
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C
5
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D
8
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Solution

The correct option is C 5
Factor of x2+3x+2=(x+1)(x+2)
Factor of x2+6x+8=(x+2)(x+4)
x(x+3)(x+1)(x+2)2(x+4)(x2+kx+6)=x(x+1)(x+2)2(x+3)(x+4)
x2+kx+6=1
x2+kx+5=0
First check with the first option when k=2
The quadratic equation becomes, imaginery roots.
For the second option when k=3, the equation becomes imaginery roots.
For the third option when k=5
The equation becomes real and distinct roots.
x=2,x=3
So, the value of k is 5.

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