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Grade 11Algebra

The integral values of k for which the roots of kx(x+2) + k – (x+2) = 0 are rational is given by -
(A) 5
(B) -3
(C) -6
(D) 12

Profile image of ankit biswal
9 Years agoGrade 11
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1 Answer

Profile image of Tanishq Chourishi
9 Years ago
the equation can be rearranged as kx2+2kx+k-x-2=0
 
kx2+x(2k-1)+k-2=0
now as the roots are rational D>=0 i.e b2-4ac>=0     for equation ax2+bx+c=0
thus 
here b=2k-1   ;a=k  ;c=k-2
(2k-1)2-4(k)(k-2)>=0
4k2-4k+1-(4k2-8k)>=0
4k2-4k+1-4k2+8k>=0
4k+1>=0
k>=-(1/4)
thus answer should be A B C D
 
 
 

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