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Let p(x)=0 be a polynomial equation of t...

Let `p(x)=0` be a polynomial equation of the least possible degree, with rational coefficients having `""^(3)sqrt7 +""^(3)sqrt49` as one of its roots. Then product of all the roots of `p(x)=0` is
a. `56` b. `63` c. `7` d. 49

A

56

B

63

C

7

D

49

Text Solution

Verified by Experts

The correct Answer is:
1
`x = ""^(3)sqrt7 + ""^(3)sqrt(49)`
`rArr x^(3) = 7 + 49 + 3root(3)(7) " "root(3)(49) (root(3)(7) + root(3)(49)) = 56 + 21x`
or `x^(3) - 21x - 56 = 0`
Therefore, the product of roots is 56.
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