Let A(x)=∣∣
∣
∣∣33x3x2+2a23x3x2+2a23x3+6a2x3x2+2a23x3+6a2x3x4+12a2x2+2a4∣∣
∣
∣∣, where a∈R is a non-zero constant. Then which of the following option(s) is/are INCORRECT ?
A
There exists x∈R such that A(x)=0
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B
A(x) is independent of x
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C
1∫−1A(x)dx=16a6
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D
Area bounded by the curve y=A(x),x=−2,x=3 and the x-axis is 20a6
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Solution
The correct options are A There exists x∈R such that A(x)=0 C1∫−1A(x)dx=16a6 A(x)=∣∣
∣
∣∣33x3x2+2a23x3x2+2a23x3+6a2x3x2+2a23x3+6a2x3x4+12a2x2+2a4∣∣
∣
∣∣