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Question

# If expression x2−4cx+b2>0for all real values of x and a2+b2<ab, then range of the function x+ax2+bx+c2 is

A
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B
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C
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D
None of these
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Solution

## The correct option is C (−∞,∞)Letis,Wehavetheequ:x2−4cx+b2>0,anditsdiscriminateis:D<0⇒16c2−4b2<0⇒4c2−b2<0Now,x+ax2+bx+c2,anddiscriminateofx2+bx+c2⇒b2−4c2>0,soitsrootsa&βthenexpressionofx+a(x−α)(x−β)[wecanunderstandthroughgraphInthisconditionthewholelineattendsto−∞to+∞.so,wecansaytherangeofy=(−∞,∞)arerealno.andthecorrectoptionisC.

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