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If x^2-2x-15=0 and x>0, which of the following must b equal to zero ?
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Updated on: 20 Apr 2022, 04:34

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If \(x^2-2x-15=0\) and \(x>0\), which of the following must be equal to zero ?

Select all that apply

A. \(x^2-6x+9\)

B. \(x^2-7x+10\)

C. \(x^2-10x+25\)

D. \(x^2+6x+9\)

E. \(x^2+7x+10\)

F. \(x^2+10x+25\)

Kudos for the right answer and explanation

Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION

GRE - Math Book

Select all that apply

A. \(x^2-6x+9\)

B. \(x^2-7x+10\)

C. \(x^2-10x+25\)

D. \(x^2+6x+9\)

E. \(x^2+7x+10\)

F. \(x^2+10x+25\)

Kudos for the right answer and explanation

Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION

GRE - Math Book

Re: If x^2-2x-15=0 and x>0, which of the following must b equal to zero ?
[#permalink]
19 Apr 2021, 19:15

1

\(x^2-2x-15=0\)

\((x-5)(x+3) = 0\)

\(x = -3\) OR \(5\)

We are given that \(x > 0\) so \(x = 5\)

By putting the value of \(x\) in the given option,

B & C will be 0

Answer B C

\((x-5)(x+3) = 0\)

\(x = -3\) OR \(5\)

We are given that \(x > 0\) so \(x = 5\)

By putting the value of \(x\) in the given option,

B & C will be 0

Answer B C

If x^2-2x-15=0 and x>0, which of the following must b equal to zero ?
[#permalink]
03 Jan 2024, 00:23

1

If \(x^2-2x-15=0\)

we can then obtain two factors \((x+3)\) and \((x-5)\). Since \(x>0\), should consider only the factor \((x-5)\).

Now, to find out which of the list of choices is equal to zero, we just have to simply find the expressions which can have at least \((x-5)\) as a factor.

Now only Choices B,C,E,F have constant terms that are multiples of \(5\), which I would expect when \((x-5)\) is a factor. But of these I will eliminate E and F, because the coefficient of the linear term is positive, when I would expect it to be negative, -7 for E, to obtain a constant term of 10, and -10 for F, to obtain a constant term of 25.

But Choices B and C offer me the very same coefficients for the linear term that I am looking for. Hence they are the correct choices.

we can then obtain two factors \((x+3)\) and \((x-5)\). Since \(x>0\), should consider only the factor \((x-5)\).

Now, to find out which of the list of choices is equal to zero, we just have to simply find the expressions which can have at least \((x-5)\) as a factor.

Now only Choices B,C,E,F have constant terms that are multiples of \(5\), which I would expect when \((x-5)\) is a factor. But of these I will eliminate E and F, because the coefficient of the linear term is positive, when I would expect it to be negative, -7 for E, to obtain a constant term of 10, and -10 for F, to obtain a constant term of 25.

But Choices B and C offer me the very same coefficients for the linear term that I am looking for. Hence they are the correct choices.

gmatclubot

If x^2-2x-15=0 and x>0, which of the following must b equal to zero ? [#permalink]

03 Jan 2024, 00:23
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