Question

Nature of Roots
Show that k(x²-x)+1-k=x²

Answer 1

$k(x ^{2} - x) + 1 - k = x ^{2} \\ kx ^{2} - kx + 1 - k - x ^{2} =0 \\ x ^{2} (k - 1) - kx +( 1 - k) = 0$

So,here a=k-1,b=-k,c=(1+k)

D=b^2-4ac

D=(-k)^2-[4×(k-1)(1+k)]

D=k^2-4(k^2-1)

D=k^2-4k^2+4

D= -3k^2+4