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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 4a−6b+9c>0Given: f(x)=ax2+bx+c From the given graph, f(x)>0, ∀x∈R Now, f(−1)>0 a(−1)2+b(−1)+c>0 ⇒a−b+c>0 Similarly, f(−2)>0 a(−2)2+b(−2)+c>0 ⇒4a−2b+c>0 f(−3)>0 a(−3)2+b(−3)+c>0 ⇒9a−3b+c>0 f(−23)>0 a(−23)2+b(−23)+c>0 ⇒4a9−2b3+c>0 ⇒4a−6b+9c>0

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