Question

$expansion \: x2 \: - 4 \: cx \: + b2 \: < 0for \: all \: reall \: values \: of \: x \: and \: a2 \: + b2 \: < \: ab \: then \: range \: of \: the \: function \: \: x \: + \: a \: \\ \: \: \: \: \: \: \: \: \: \: \: \: x \: 2 \: + \: bx \: + \: c2 \: is \: =$
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Answer 1

Letis,

Wehavetheequ:x

2

−4cx+b

2

>0,

anditsdiscriminateis:D<0

⇒16c

2

−4b

2

<0

⇒4c

2

−b

2

<0

Now,

x

2

+bx+c

2

x+a

,anddiscriminateofx

2

+bx+c

2

⇒b

2

−4c

2

>0,soitsrootsa&β

thenexpressionof

(x−α)(x−β)

x+a

[wecanunderstandthroughgraph

Inthisconditionthewholelineattendsto−∞to+∞.

so,wecansaytherangeofy=(−∞,∞)arerealno.andthecorrectoptionisC.