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Question

Consider the graph of the quadratic polynomial y=ax2+bx+c as shown below.

Which among the following is/are correct?

A
ab+cabc=0
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B
abc(9a+3b+c)<0
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C
a+3b+9cabc<0
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D
abc(a3b+9c)>0
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Solution

The correct options are
A ab+cabc=0
C a+3b+9cabc<0

From the given graph,
a<0,b2a>0b>0f(0)=c>0abc<0

Now,
f(1)=0ab+c=0,f(3)=09a+3b+c=0

Clearly,
f(13)>0
a+3b+9c>0
And
f(13)>0
a9b3+c>0a3b+9c>0

So,
ab+cabc=0abc(9a+3b+c)=0a+3b+9cabc<0abc(a3b+9c)<0

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