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

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Joined: 04 Jan 2015
Posts: 2568
Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

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25 Jan 2019, 05:20
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Difficulty:

45% (medium)

Question Stats:

50% (03:28) correct 50% (03:50) wrong based on 30 sessions

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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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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

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

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

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
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Joined: 15 Jan 2019
Posts: 1
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

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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

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