tmua 2017 Q19

tmua · Uk · paper2 1 marks Discriminant and conditions for roots Parameter range for specific root conditions (location/count)

Which one of the following is a sufficient condition for the equation $x ^ { 3 } - 3 x ^ { 2 } + a = 0$, where $a$ is a constant, to have exactly one real root?
A $a > 0$
B $a \leqslant 0$
C $\quad a \geqslant 4$
D $a < 4$
$\mathbf { E } \quad | a | > 4$
$\mathbf { F } \quad | a | \leqslant 4$
G $\quad a = \frac { 9 } { 4 }$
$\mathbf { H } \quad | a | = \frac { 3 } { 2 }$

& D

Which one of the following is a sufficient condition for the equation $x ^ { 3 } - 3 x ^ { 2 } + a = 0$, where $a$ is a constant, to have exactly one real root?

A $a > 0$

B $a \leqslant 0$

C $\quad a \geqslant 4$

D $a < 4$

$\mathbf { E } \quad | a | > 4$

$\mathbf { F } \quad | a | \leqslant 4$

G $\quad a = \frac { 9 } { 4 }$

$\mathbf { H } \quad | a | = \frac { 3 } { 2 }$

Paper Questions

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