Concept: For a quadratic equation ax2+bx+c=0 The sum of the roots =−
b
a
The product of the roots =
c
a
Calculation: Let the other root be α Given equation is x(x+1)+1=0 x2+x+1=0 a=1,b=1 and c=1 As k is the root of the equation k2+k+1=0 k2=−k−1 The sum of the roots =−
1
1
=−1 Second root is α. α+k=−1 α=−1−k From equation (i) α=k2 ∴ The other root =k2