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If one root of the equation x 2 − 5x + m = 0 is 10, what is the value

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If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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New post 24 Jan 2016, 06:03
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Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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Hi All,

As you perform at higher levels on the GMAT, the test will throw you questions based on subjects that you know, but in ways that you're probably not used to thinking about. This question is based on Quadratics, but you have to organize the information 'backwards', using an end result to reconstruct the original equation.

We're told that one root of the equation X^2 − 5X + m = 0 is 10. We can now start to reverse-FOIL this equation....

X^2 - 5X + M = 0
(X-10)(X + ?) = 0

Since the sum of the "O" and "I" in foil is -5X, we can set up the following equation:

-10X + ?X = -5X
?X = 5X
This proves that the missing 'number' in the above equation is 5...

(X-10)(X+5) = 0
X^2 - 10X + 5X - 50 = 0
X^2 - 5X - 50 = 0

The question asks for the value of M + 3. Since M = -50, (M+3) = -47.

Final Answer:
[Reveal] Spoiler:
D


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Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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For a quadratic equation if one of roots is given then it satisfies the equation
In equation \(x^2\)\(-\)\(5x\)\(+\)\(m\) = \(0\) , one of the root is given as 10

Substitute \(x\) = \(10\) in the above equation we get
\(10^2\)\(-\)\(5*10\)\(+\)\(m\) = 0

\(m\) =\(-50\)
\(m+3\) = \(-50 + 3\) =\(-47\)

Correct Answer - D
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Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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New post 15 Jun 2016, 04:07
Bunuel wrote:
If one root of the equation x^2 − 5x + m = 0 is 10, what is the value of m + 3?

A. 50
B. 10
C. −5
D. −47
E. −50



From given equation

Sum of roots = (5/1) = 5 ..................(1)
Product of roots = m......................(2)

One of the roots is 10. Therefor from (1), other root is -5.

m = (10) (-5) = -50
m+3 = -47

D is the answer
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Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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New post 09 Apr 2018, 09:37
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Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value   [#permalink] 09 Apr 2018, 09:37
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