For the equation `3x^2+p x+3=0,p >0,` if one of the root is square of the other, then `p` is equal to `1//3` b. `1` c. `3` d. `2//3`

Options

A. `(1)/(3)`
B. 1
C. 3
D. `2//3`

Answer

C

Explanation

Let `alpha and alpha^(2)` be the roots of the given equation. Then, `alpha + alpha^(2) = - p//3 and alpha^(3) = 1`
Now, `alpha^(3) = 1 rArr alpha = 1, omega, omega^(2)`
Thus the roots of the given equation are `omega and omega^(2)`. Therefore, `alpha = omega`.
Now,
`therefore" "alpha + alpha^(2) = - (p)/(3) rArr omega + omega^(2) = - (p)/(3) rArr -1 = - (p)/(3) rArr p = 3`