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Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then

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Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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New post Updated on: 06 Jul 2019, 05:25
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Let \(C\) and \(K\) be constants.If \(x^2+Kx+5\) factors into \((x+1)*(x+C)\), then what is the value of \(K\)?

A)0
B)5
C)6
D)8
E)Cannot be determined

Source: Nova GMAT
Difficulty Level: 550
Spoiler: OA

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Originally posted by stonecold on 22 Apr 2017, 13:02.
Last edited by SajjadAhmad on 06 Jul 2019, 05:25, edited 1 time in total.
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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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New post 22 Apr 2017, 16:35
Matching constants value on the given equation with its factor ... we get C=5 and K=c+1=6
Option C

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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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New post 26 Jun 2017, 05:21
we have been given that X^2+kx+5 in to factor equtations (x+1) (x+c)
now solve this (x+1) (x+c) = x^2+x+cx+c
x^2 +x(1+c) + c
Now we know that equation is x^2 +kx+5 form so compare this equation with x^2 +X(1+c) + C
we will comclude that c=5, kx will be = x(1+c) i.e. 6x since c=5
so the value of k=6
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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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New post 26 Jun 2017, 05:36
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For the quadratic equation \(x^2\)+Kx+5; sum of roots = K and product of roots = 5

Roots given as (x+1) and (x+C)
Hence, product of the roots = 1*C = 5
Hence C=5

Sum of the roots = K = 1+5 = 6
Answer C
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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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New post 27 Jun 2017, 07:32
stonecold wrote:
Let \(C\) and \(K\) be constants.If \(x^2+Kx+5\) factors into \((x+1)*(x+C)\), then what is the value of \(K\)?

A)0
B)5
C)6
D)8
E)Cannot be determined

Source => NOVA.

Because we are given one factor's integer, (x+1), I would just factor \(x^2+Kx+5\).

With (x+1) and (x + ___), thinking about FOIL where last two terms multiplied must equal 5, we need:

1*__ = 5. 1*5 = 5. Write the factors and multiply.

(x+1)(x+5) = \(x^2 + 6x + 5\).

K = 6, Answer C.
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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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New post 27 Jun 2017, 13:24
Let \(C\) and \(K\) be constants.If \(x^2+Kx+5\) factors into \((x+1)*(x+C)\), then what is the value of \(K\)?

\(x^2+Kx+5\) = \((x+1)*(x+C)\)

As we know that \(a^2 + 2ab + b^2\) = \((a+b) * (a+b)\)

After comparing the above equation with our equation we can see that

b = c = 5

We can also directly equate \(2ab = kx = 6x\)- However in order to make it more clear we will understand in detail per below steps.

\(x^2+Kx+5\) = \(x^2 + 5x + 1x + 5\)

\(x^2+Kx+5\) = \(x^2 + 6x + 5\)

\(kx = 6x\)

\(k = 6\)

Hence, the answer is C
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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then  [#permalink]

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Re: Let C and K be constants.If x^2+Kx+5 factors into (x+1)(x+C), then   [#permalink] 01 Oct 2018, 07:16
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