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# If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

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If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

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Updated on: 11 Sep 2018, 23:37
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65% (hard)

Question Stats:

43% (01:31) correct 57% (01:56) wrong based on 24 sessions

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If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

(1) Both roots are prime number
(2) 2 is one of root of the equation

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Originally posted by GMATbuster92 on 11 Sep 2018, 23:36.
Last edited by Bunuel on 11 Sep 2018, 23:37, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
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If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

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11 Sep 2018, 23:43
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:

$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

(1) Both roots are prime number.

According to the theorem: $$x_1+x_2=\frac{-b}{a}=7$$. 7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.

(2) 2 is one of root of the equation. Plug x = 2: 2^2 − 7*2 + k = 0. We can find k. Sufficient.

Hope it's clear.
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Re: If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

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12 Sep 2018, 00:32
Bunuel wrote:
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:

$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

(1) Both roots are prime number.

According to the theorem: $$x_1+x_2=\frac{-b}{a}=7$$. 7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.

(2) 2 is one of root of the equation. Plug x = 2: 2^2 − 7*2 + k = 0. We can find k. Sufficient.

Hope it's clear.

can you explain why the sum has been taken as 7 and not 5? (3+2)
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Joined: 02 Sep 2009
Posts: 55277
Re: If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

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12 Sep 2018, 00:35
rahulkashyap wrote:
Bunuel wrote:
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:

$$x_1+x_2=\frac{-b}{a}$$AND $$x_1*x_2=\frac{c}{a}$$.

(1) Both roots are prime number.

According to the theorem: $$x_1+x_2=\frac{-b}{a}=7$$.7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.

(2) 2 is one of root of the equation. Plug x = 2: 2^2 − 7*2 + k = 0. We can find k. Sufficient.

Hope it's clear.

can you explain why the sum has been taken as 7 and not 5? (3+2)

$$x_1+x_2=\frac{-b}{a}=\frac{-(-7)}{1}=7$$.
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Re: If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?   [#permalink] 12 Sep 2018, 00:35
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