jee-advanced 2010 Q31

jee-advanced · India · paper2 Curve Sketching Number of Solutions / Roots via Curve Analysis

Consider the polynomial
$$f ( x ) = 1 + 2 x + 3 x ^ { 2 } + 4 x ^ { 3 }$$
Let s be the sum of all distinct real roots of $\mathrm { f } ( \mathrm { x } )$ and let $\mathrm { t } = | \mathrm { s } |$.
The real number $s$ lies in the interval
A) $\left( - \frac { 1 } { 4 } , 0 \right)$
B) $\left( - 11 , - \frac { 3 } { 4 } \right)$
C) $\left( - \frac { 3 } { 4 } , - \frac { 1 } { 2 } \right)$
D) $\left( 0 , \frac { 1 } { 4 } \right)$

Consider the polynomial

$$f ( x ) = 1 + 2 x + 3 x ^ { 2 } + 4 x ^ { 3 }$$

Let s be the sum of all distinct real roots of $\mathrm { f } ( \mathrm { x } )$ and let $\mathrm { t } = | \mathrm { s } |$.

The real number $s$ lies in the interval\\
A) $\left( - \frac { 1 } { 4 } , 0 \right)$\\
B) $\left( - 11 , - \frac { 3 } { 4 } \right)$\\
C) $\left( - \frac { 3 } { 4 } , - \frac { 1 } { 2 } \right)$\\
D) $\left( 0 , \frac { 1 } { 4 } \right)$

Paper Questions

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