1
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1

Consider the polynomial
$$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$
Let $$s$$ be the sum of all distinct real roots of $$f(x)$$ and let $$t = \left| s \right|.$$

The real numbers lies in the interval

A
$$\left( { - {1 \over 4},0} \right)$$
B
$$\left( { - 11, - {3 \over 4}} \right)$$
C
$$\left( { - {3 \over 4}, - {1 \over 2}} \right)$$
D
$$\left( {0,{1 \over 4}} \right)$$
2
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1

Consider the polynomial
$$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$
Let $$s$$ be the sum of all distinct real roots of $$f(x)$$ and let $$t = \left| s \right|.$$

The function$$f'(x)$$ is

A
increasing in $$\left( { - t, - {1 \over 4}} \right)$$ and decreasing in $$\left( { - {1 \over 4},t} \right)$$
B
decreasing in $$\left( { - t, - {1 \over 4}} \right)$$ and increasing in $$\left( { - {1 \over 4},t} \right)$$
C
increasing in $$(-t, t)$$
D
decreasing in $$(-t, t)$$
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