Question

Find the value of k if the equation 3x2-kx+2=0 has equal roots.

Answer 1

hi!

The value of k is 2√6.

hope this helps ! !#

Answer 2

The values of k when roots are equal are 2√6 and -2√6.

We have to find the value of k if the equation 3x² - kx + 2 = 0 has equal roots.

Let α and β are roots of given equation.

∵ both roots of equation are equal.

∴ α = β ...(1)

now sum of roots = - coefficient of x/coefficient of x²

⇒α + β = -(-k)/3

⇒ α + α = 2α = k/3

⇒α = k/6 ...(2)

product of roots = constant/coefficient of x²

⇒αβ = 2/3

⇒α × α = α² = 2/3

⇒α = ±√(2/3)

from equation (2),

⇒±√(2/3) = k/6

⇒k = ±6√(2/3) = ±2√6

Therefore the value of k is ±2√6.