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Question

If one root of the equation x2+ax+12=0 is 4 while the equation x2+ax+b=0 has equal roots, then the value of b is


A

449

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B

494

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C

74

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D

47

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Solution

The correct option is B

494


Explanation for the correct option.

Step 1: Calculation for the value of a.

As the root of the equation x2+ax+12=0 is 4 then to find the value of the a put x=4 in the same equation,

āˆ“42+4a+12=0ā‡’28+4a=0ā‡’a=-7

Apply this value to the equation x2+ax+b=0.

Step 2: Calculation for the value of b.

To find the value of b we have the equation x2-7x+b=0 with equal roots.

For the equal roots, we know that the discriminant D is equal to 0.

āˆ“D=B2-4AC, where B=-7,A=1,andC=b

āˆ“B2-4AC=0ā‡’-72-41b=0ā‡’4b=49ā‡’b=494

Hence, the correct option is (B).


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