Question

sum of squares of the roots of the equation
x² - 2kx +(2k+1) = 0 is 6

Answer 1

Answer:

K= 2 OR -1

Step-by-step explanation:

LET α,β ARE THE ROOTS OF THE EQUATION

x²-2kx+(2k+1)=0

α + β= 2k...............(i)

αβ = 2k+1................(ii)

IT IS GIVEN,

α²+β²=6

⇒(α+β)²-2αβ=6

⇒4k²-4k-2=6

⇒4k²-4k-8=0

⇒4k²-8k+4k-8=0

⇒4k(k-2)+4(k-2)=0

⇒(k-2)(4k+4)=0

THEREFORE, K= 2 OR -1