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Assertion :If a>0 and b2−4ac<0. then the value of the integral ∫dxax2+bx+c will be of the type μtan−1(x+AB)+C; where A,B,C,μ are constant. Reason: If a>0,b2−4ac<0, then ax2+bx+c can be written as sum of two squares.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
If a>0 and b24ac<0, then
ax2+bx+c=a(x+b2a)2+4acb24a
dxax2+bx+c=dxa(x+b2a)+k2
where k2=4acb24a>0
which will of the type 1a.1katan1x+b2aka+C=μtan1(x+AB)+C
where μ=1ak,A=b2a,B=ka are constants

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