tmua 2018 Q15

tmua · Uk · paper2 1 marks Curve Sketching Number of Solutions / Roots via Curve Analysis

It is given that $\mathrm { f } ( x ) = x ^ { 3 } + 3 q x ^ { 2 } + 2$, where $q$ is a real constant.
The equation $\mathrm { f } ( x ) = 0$ has 3 distinct real roots.
Which of the following statements is/are necessarily true?
I The equation $\mathrm { f } ( x ) + 1 = 0$ has 3 distinct real roots.
II The equation $\mathrm { f } ( x + 1 ) = 0$ has 3 distinct real roots.
III The equation $\mathrm { f } ( - x ) - 1 = 0$ has 3 distinct real roots.

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It is given that $\mathrm { f } ( x ) = x ^ { 3 } + 3 q x ^ { 2 } + 2$, where $q$ is a real constant.

The equation $\mathrm { f } ( x ) = 0$ has 3 distinct real roots.

Which of the following statements is/are necessarily true?

I The equation $\mathrm { f } ( x ) + 1 = 0$ has 3 distinct real roots.

II The equation $\mathrm { f } ( x + 1 ) = 0$ has 3 distinct real roots.

III The equation $\mathrm { f } ( - x ) - 1 = 0$ has 3 distinct real roots.

Paper Questions

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