Given,
2 is as root of 3x2 + px -8 = 0
So, on substituting x = 2 the LHS will become zero and satisfy the equation.
⇒ 3(2)2 + p(2) – 8 = 0
⇒ 12 + 2p – 8 = 0
⇒ 4 + 2p = 0
⇒ p = -2
Now, substituting the value of p in the second equation we have
4x2 – 2(-2)x + k = 0
⇒ 4x2 + 4x + k = 0
It’s given that the above equation has equal roots.
Thus the discriminant, D = 0
The equation 4x2 + 4x + k = 0 is in the form of ax2 + bx + c = 0
Where a = 4, b = 4, c = k
D = b2 – 4ac
⇒ 42 – 4(4)(k) = 0
⇒ 16 – 16k = 0 [dividing by 16 both sides]
⇒ k = 1
Therefore, the value of k is 1.