UPSC NDA I 2021 Mathematics Solved Paper

Concept
Let us consider the standard form of a quadratic equation, ax2+bx+c=0
Let α and β be the two roots of the above quadratic equation.
The sum of the roots of a quadratic equation is given by: α+β=−‌

b

a

=−‌

‌ coefficient of ‌x

‌ coefficient of ‌x2

The product of the roots is given by: αβ=‌

c

a

=‌

‌ constant term ‌

‌ coefficient of ‌x2

Calculation:
Let α be a one root of given polynomial
then, other root will be ‌

1

α

Given: 5x2+26x+k=0
Compare with general equation ax2+bx+c=0
a=5,b=26,c=k
Products of root =‌

c

a

α×‌

1

α

=‌

k

5

k=5
The value of k is 5