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Question

If a, b, c ϵ R and a 0, c > 0, the graph of f(x) = ax2+bx+c for which f(x)=0 has only imaginary roots, will look like


A

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B

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C

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D

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Solution

The correct option is A


Given f(x) = ax2+bx+c has imaginary roots

D < 0

b24ac < 0

b2< 4ac

As b ϵ R, b2 is always > 0 and for 4ac > b2, 4ac should be > 0

a & c should have same sign

As c > 0, a> 0

Hence as a > 0 and D < 0, graph is bowl shaped and don't touch x-axis f(x) is always positive.

So, A is right option


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