UPSC NDA I 2021 Mathematics Solved Paper

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