UPSC CDS 1 2022 Math Paper

Given:
x2+αx+β=0
α and β are the roots of above equation
Concept Used:
For equation ax2+bx+c=0
Sum of roots =−b∕a
Product of roots =c∕a
Calculation:
The given equation is x2+αx+β=0
Here, a=1,b=α,c=β
Sum of roots (α+β)=−α∕1
⇒2α+β=0‌‌⋯‌ (i) ‌
Product of roots (α.β)=β∕1
⇒α=1
From (i) and (ii), we get
β=−2‌‌⋯−(‌ iii) ‌
Now, we have to find the value of α−β
⇒α−β=1−(−2)=3
∴ The required value of α−β is 3 .