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Question

If x2 and x12 both are the factors of the polynomial nx25x+m, then m=n=2

A
True
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B
False
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Solution

The correct option is A True
Let f(x)=nx25x+m
x2 and x1/2 are factors of f(x) then x=2 and x=12 are roots of
equation f(x)
Now, we know
Product of roots = mn=(2)×(12)
mn=1
m=n
and
sum of roots = (5)=2+12=52
5n=52n=2
m=n=2 Hence proved

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