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Question of the week - 33 (A quadratic equation is in the form ......)

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Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

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New post 25 Jan 2019, 05:20
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  45% (medium)

Question Stats:

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A quadratic equation is in the form of \(x^2 – 2px + m = 0\), where m is divisible by 5 and is less than 120. One of the roots of this equation is 7. If p is a prime number and one of the roots of the equation, \(x^2 – 2px + n = 0\) is 12, then what is the value of p + n – m?

    A. 0
    B. 6
    C. 16
    D. 26
    E. 27

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Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

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New post 25 Jan 2019, 05:30
\(x^2–2px+m=0\)
and m is divisible by 5.
And one of the roots = 7.
Put x = 7
49-14p+m = 0
and also, P is prime.
Only number which satisfies the equation is for p = 11
Then 49-154+m = 0
m = 105.

Now, \(x^2–2px+n=0\) has one root as x = 12
Then 144-24p+n = 0
p = 11
Then n = 120

p+n-m = 11+120-105 = 26

D is the answer.
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Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

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New post 25 Jan 2019, 22:50
D is the answer using the concept of S.o.r and p.o.r.

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Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

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New post 27 Jan 2019, 09:03
Afc0892 wrote:
\(x^2–2px+m=0\)
and m is divisible by 5.
And one of the roots = 7.
Put x = 7
49-14p+m = 0
and also, P is prime.
Only number which satisfies the equation is for p = 11
Then 49-154+m = 0
m = 105.

Now, \(x^2–2px+n=0\) has one root as x = 12
Then 144-24p+n = 0
p = 11
Then n = 120

p+n-m = 11+120-105 = 26

D is the answer.


how do u came to conclusion p=11?
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Re: Question of the week - 33 (A quadratic equation is in the form ......)   [#permalink] 27 Jan 2019, 09:03
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Question of the week - 33 (A quadratic equation is in the form ......)

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