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Question

If one root of x2+ax+8=0 is 4 and the equation x2+ax+b=0 has equal roots, then b=

A
7
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B
9
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C
1
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D
3
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Solution

The correct option is A 9
x2+ax+8=0 has one of it roots as 4
42+4a+8=0
4[4+a+2]=0
6+a=0
a=6
Now, the equation
x2+ax+b=0
x26x+b=0
has double ( equal ) roots.
In a quadratic equation, the roots will be equal if and only if the discrimination (D)=0
Now, the discriminant of the above quadratic equation is
D=B24AC=0
6241b=0
62=4b
b=364=9
a=6 and b=9
Hence, the answer is 9.


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