UPSC CDS 2 2022 Math Paper

Quadratic Equation:- A quadratic equation is a second order equation written as ax2+bx+c=0 where a,b and c are coefficients of real numbers and a≠0.
If α and β are the roots of the quadratic equation
Sum of roots;- α+β=‌

−b

a

logaxm=mlogax

We have,
⇒log10[995+√x2−12x+60]=3
⇒log10[995+√x2−12x+60]=log10103
⇒995+√x2−12x+60=103
⇒995+√x2−12x+60=1000
⇒√x2−−12x+60=5
On squaring both the sides, we get
⇒x2−12x+60=25
⇒x2−12x+35=0
⇒‌ Sum of roots ‌=‌

−(−12)

1

=12