Question

Suppose for fixed real numbers a and b.$f\left(x\right)=x^3+a{x}^2+bx+c$, has 3 distinct roots for c =0. Then

• A. $f_c$ has 3 distinctroots for all real c
• B. $f_c\left(x\right)$ has 3 distinct roots for all real c>o or for all real c<0, but not for both
• C. $f_c\left(x\right)$ has 3 distinct roots for all real c in (p,q) for some p<0 and q>0
• D. $f_c\left(x\right)$ need not have 3 distinct roots for any real c other than zero

Answer 1

Answer: (D)

$f_c\left(x\right)$ need not have 3 distinct roots for any real c other than zero

$f\left(x\right)=x^3+a{x}^2+bx+c$
Since f(x) has three roots when c = 0