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Question

Assertion :If a,b,cR and equations ax2+bx+c=0 & x2+3x+4 have a common root then a+cb=43. Reason: If both roots of ax2+bx+c=0 and a′′x2+b′′x+c′′=0 are identical then aa′′=bb′′=cc′′ where a,b,c,′′b,′′c,R.

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
Assertion is incorrect but Reason is correct
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Solution

The correct option is D Assertion is incorrect but Reason is correct
Given equations, ax2+bx+c=0
x2+3x+4=0Here, D=916=7<0 , so complex roots.
Since, roots of x2+3x+4=0 are complex roots , both roots are common.
For common roots,a1=b2=c4=λ (say)
a=λ,b=3λ,c=4λ
a+cb=5λ3λ=5343.Hence, assertion is not true.
If both roots of ax2+bx+c=0 and a′′x2+b′′x+c′′=0 are identical,
then aa′′=bb′′=cc′′ where a,b,c,′′b,′′c,R which is the condition for both roots common.
Hence, reason is true.

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