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Question

If the equation x510a3x2+b4x+c5=0 has 3 equals roots, then

A
2b210a3b2+c5=0
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B
6a5+c5=0
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C
2c510a3b2+b4c5=0
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D
b4=15a4
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Solution

The correct options are
B 6a5+c5=0
D b4=15a4
f(x)=x510a3x2+b4x+c5
f(x)=5x420a320a3x+b4
f′′=20x320a3
If x=α be a root that is repeated 3 times, then f′′(α)=0 and f(α)=0
α=a,5a420a4+b4=0
a510a5+ab4+c5=0
α=a,b4=15a4 and 6a5+c5=0

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