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Question

If both the roots of the quadratic equation x22px+p2+p5=0 are less than 3, then k lies in the interval

A
(,1)
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B
(1,)
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C
(1,3)
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D
(3,)
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Solution

The correct option is A (,1)
wehavex22px+ph2+p5=0xisrealthen,D04p24.1.(p2+p5)04p24p24p+2004p20p5(1)f(3)>0(bothrootsarelessthan3)323p.3+p2+p5>096p+p2+p5>0p25p+4>0(p1)(p4)>0thenI(,1)(4,)(2)alsoα+β<32p<3p<32(3)byequn(1),(2),&(3)wegetp(,1).Hence,optionAisthecorrectanswer.

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