tmua 2023 Q19

tmua · Uk · paper2 1 marks Factor & Remainder Theorem True/False or Multiple-Statement Evaluation

In this question, $f ( x )$ is a non-constant polynomial, and $g ( x ) = x f ^ { \prime } ( x )$ $f ( x ) = 0$ for exactly $M$ real values of $x$. $g ( x ) = 0$ for exactly $N$ real values of $x$. Which of the following statements is/are true? I It is possible that $M < N$ II It is possible that $M = N$ III It is possible that $M > N$
A none of them B I only C II only D III only E I and II only F I and III only G II and III only H I, II and III

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In this question, $f ( x )$ is a non-constant polynomial, and $g ( x ) = x f ^ { \prime } ( x )$
$f ( x ) = 0$ for exactly $M$ real values of $x$.
$g ( x ) = 0$ for exactly $N$ real values of $x$.
Which of the following statements is/are true?
I It is possible that $M < N$
II It is possible that $M = N$
III It is possible that $M > N$

A none of them
B I only
C II only
D III only
E I and II only
F I and III only
G II and III only
H I, II and III

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20