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How many positive integral values of P are possible, if f(x)= x^2-8x+

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Joined: 19 Oct 2018
Posts: 1171
Location: India
How many positive integral values of P are possible, if f(x)= x^2-8x+  [#permalink]

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28 Nov 2019, 08:41
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Difficulty:

55% (hard)

Question Stats:

46% (01:50) correct 54% (01:50) wrong based on 28 sessions

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How many positive integral values of P are possible, if $$f(x)= x^2-8x+P$$, and f(1) and f(2) are opposite in sign ?

A. 0
B. 2
C. 3
D. 4
E. 6
Math Expert
Joined: 02 Aug 2009
Posts: 8305
Re: How many positive integral values of P are possible, if f(x)= x^2-8x+  [#permalink]

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29 Nov 2019, 00:29
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nick1816 wrote:
How many positive integral values of P are possible, if $$f(x)= x^2-8x+P$$, and f(1) and f(2) are opposite in sign ?

A. 0
B. 2
C. 3
D. 4
E. 6

$$f(x)= x^2-8x+P$$.......$$f(1)= 1^2-8*1+P=P-7$$ and $$f(2)= 2^2-8*2+P=P-12$$
Two cases for opposite sign
(I) f(1)>0 and f(2)<0
P-7>0...P>7
P-12<0...P<12
7<P<12
Integral solutions of P are 8, 9, 10 and 11 ----So 4 integral values
(II) f(1)<0 and f(2)>0
P-7<0...P<7
P-12>0...P>12
P<7 and P>12...No solution possible as both range do not have any common values.

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Re: How many positive integral values of P are possible, if f(x)= x^2-8x+   [#permalink] 29 Nov 2019, 00:29
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