UPSC CDS 2 2021 Math Paper

Given, quadratic equation is
x2−kx+2=0.
In a quadratic equation
ax2+bx+c=0,
if ‌‌ the D=b2−4ac>0,‌‌ discriminant, quadratic equation will have real and distinct solutions.
For x2−kx+2=0
∴b2−4ac=(−k)2−4(1)(2)
‌‌=k2−8 Put b2−4ac>0⇒k2−8>0
⇒k2−(2√2)2>0
⇒(k−2√2)(k+2√2)>0
∴k<−2√2 or k>2√2
Hence, the quadratic equation will have real and distinct solutions for
k<−2√2 or k>2√2.