Question

Find the non-zero value of k,for which the quadratic equation kxsquare+1-2(k-1)x+xsquare =0 has equal roots.hence find the roots of the equation

Answer 1

Answer:

the equation has equal roots then

D=0

x^2(k+1) -2x(k-1) +k=0

D is

4(k^2+1-2k) -4k(k+1)=0

4k^2-8k+4-4k^2-4k=0

-12k=-4

k=1/3

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Answer 2

Answer:

kx^2+1-2(k-1) x+x^2

a=k+1

b=-2(k-1)

c=1

b^2-4ac=0

[-2(k-1)]^2-4(k+1) (1) =0

4[(k-1) ^2-(k-1)]=0

4(k^2-3k+0) =0

k(k-3) =0

k=3 or k=0