Complex Numbers And Quadratic Equations question 468
Question: Let p(x) =0 be a polynomial equation of the least possible degree, with rational coefficients, having $ \sqrt[3]{7}+\sqrt[3]{49} $ as one of its roots. Then the product of all the roots of p(x)=0 is
Options:
A) 56
B) 63
C) 7
D) 49
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ x=\sqrt[3]{7}+\sqrt[3]{49} $
$ \Rightarrow x^{3}=7+49+3\sqrt[3]{7}\sqrt[3]{49}(\sqrt[3]{7}+\sqrt[3]{49})=56+21x $ Or $ x^{3}-21x-56=0 $ Therefore, the product of roots is 56.
BETA
