SSC CHSL 2020 PYQ — Question 55

Understanding

Tricks

Application

√6x² – kx + √6 = 0

Since sinθ and secθ are roots of the equation. 

So, sinθ(secθ) = tanθ = √6/√6 = 1

(Because, if p and q are roots of ax² + bx + c = 0, then, pq = c/a)

So, θ = 45^o

Now,

x² - (sin45^o + sec45^o)x + tan45^o

⇒ x² - (1/√2 + √2)x + 1

⇒ x² - (3/√2)x + 1

⇒ √6x² - √6(3/√2)x + √6

⇒ √6x² - (3√3)x + √6

Hence

Comparing it with √6x² – kx + √6 = 0, we get, 

k = 3√3