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Question

The condition for y=ax4+bx3+cx2+dx+e to have points of inflection is

A
b24ac>0
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B
3b28ac=0
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C
3b28ac>0
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D
3b28ac<0
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Solution

The correct option is C 3b28ac>0
f′′(x)=0 for inflection point.
f(x)=4ax3+3bx2+2cx
f′′(x)=12ax2+6bx+2c=0
Roots of this equation will be
x=3b±9b224ac12a
So 9b224ac>0
3b28ac>0

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