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Question

The graph of a quadratic polynomial f(x)=ax2+bx+c is shown below


Which of the following options is/are true for the graph?

A
9a3b+c<0
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B
4a2b+c<0
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C
ab+c>0
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D
4a6b+9c>0
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Solution

The correct option is D 4a6b+9c>0
Given: f(x)=ax2+bx+c

From the given graph,
f(x)>0, xR
Now,
f(1)>0
a(1)2+b(1)+c>0
ab+c>0

Similarly,
f(2)>0
a(2)2+b(2)+c>0
4a2b+c>0

f(3)>0
a(3)2+b(3)+c>0
9a3b+c>0

f(23)>0
a(23)2+b(23)+c>0
4a92b3+c>0
4a6b+9c>0

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