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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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Math Expert
Joined: 02 Sep 2009
Posts: 47039
If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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24 Jan 2016, 06:03
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Difficulty:

5% (low)

Question Stats:

85% (00:50) correct 15% (01:10) wrong based on 89 sessions

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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

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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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25 Jan 2016, 10:55
1
1
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.

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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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15 Jun 2016, 03:47
1
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

$$m$$ =$$-50$$
$$m+3$$ = $$-50 + 3$$ =$$-47$$

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Joined: 18 Jan 2010
Posts: 254
Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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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

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Posts: 7275
Re: If one root of the equation x 2 − 5x + m = 0 is 10, what is the value [#permalink]

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09 Apr 2018, 09:37
Hello from the GMAT Club BumpBot!

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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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