tmua 2023 Q18

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

The equation $x ^ { 4 } + b x ^ { 2 } + c = 0$ has four distinct real roots if and only if which of the following conditions is satisfied?
A $b ^ { 2 } > 4 c$ B $b ^ { 2 } < 4 c$ C $c > 0$ and $b > 2 \sqrt { c }$ D $c > 0$ and $b < - 2 \sqrt { c }$ E $\quad c < 0$ and $b < 0$ F $\quad c < 0$ and $b > 0$

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The equation $x ^ { 4 } + b x ^ { 2 } + c = 0$ has four distinct real roots if and only if which of the following conditions is satisfied?

A $b ^ { 2 } > 4 c$
B $b ^ { 2 } < 4 c$
C $c > 0$ and $b > 2 \sqrt { c }$
D $c > 0$ and $b < - 2 \sqrt { c }$
E $\quad c < 0$ and $b < 0$
F $\quad c < 0$ and $b > 0$

Paper Questions

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