10. Let $f ( x )$ and $g ( x ) = x ^ { 3 } + x ^ { 2 } - 2$ be real coefficient polynomials with a common factor of degree greater than 0. Which of the following statements are correct? (1) $g ( x ) = 0$ has exactly one real root (2) $f ( x ) = 0$ must have a real root (3) If $f ( x ) = 0$ and $g ( x ) = 0$ have a common real root, then this root must be 1 (4) If $f ( x ) = 0$ and $g ( x ) = 0$ have a common real root, then the greatest common divisor of $f ( x )$ and $g ( x )$ is a linear polynomial (5) If $f ( x ) = 0$ and $g ( x ) = 0$ have no common real roots, then the greatest common divisor of $f ( x )$ and $g ( x )$ is a quadratic polynomial
& 135 & & 22 & 3 & \multirow{6}{*}{H} & 38 & －
10. Let $f ( x )$ and $g ( x ) = x ^ { 3 } + x ^ { 2 } - 2$ be real coefficient polynomials with a common factor of degree greater than 0. Which of the following statements are correct?\\
(1) $g ( x ) = 0$ has exactly one real root\\
(2) $f ( x ) = 0$ must have a real root\\
(3) If $f ( x ) = 0$ and $g ( x ) = 0$ have a common real root, then this root must be 1\\
(4) If $f ( x ) = 0$ and $g ( x ) = 0$ have a common real root, then the greatest common divisor of $f ( x )$ and $g ( x )$ is a linear polynomial\\
(5) If $f ( x ) = 0$ and $g ( x ) = 0$ have no common real roots, then the greatest common divisor of $f ( x )$ and $g ( x )$ is a quadratic polynomial