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If 2 + isqrt3 is a root of x^(3) - 6x^(2...

If `2 + isqrt3` is a root of `x^(3) - 6x^(2) + px + q = 0` (where `p` and `q` are real) then `p + q` is

Text Solution

Verified by Experts

The correct Answer is:
`1`
`alpha = 2 + i sqrt(3)`
`beta = 2 - i sqrt(3)`
so `alpha + beta + gamma = +6`
`gamma = 2`
`alphabeta + betagamma + gammaalpha = p, alphabetagamma = -q`
`7 + 2 (4) = p, q = -14`.
`rArr p = 15`
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