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I came across this in an Engineering entrance book, What is the range of this: $a^2 \sin^2 x + b \sin x \cos x + c \cos^2 x$

What is the method to find it? I tried the graph approach but didn't know how to proceed.

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    It's an oddly posed question: why is the first coefficient squared, but not the others?2012-10-27

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