If (x +9) is one of the factors of x2 + mx 4c = 0 and m and c are

Question

If (x+9) is one of the factors of x ^2  + mx – 4c = 0 and m and c are positive integers, then which of the following can be a possible value of m x c?

A. 0

B. 9

C. 27

D. 36

E. 45

gmatophobia · Answer

x = -9 is one of the roots

(-9)^2 + (-9)m – 4c = 0

81 = 9m + 4c

4c = 80 + 1 - 8m - m

c = 20 - 2m + \frac{1 - m}{4}

Assume m = 5

c = 20 - (2*5) + \frac{1 - 5}{4}

c = 20 - 10 - 1 =9

m*c = 45

Option E

Kinshook · Answer

Asked: If (x+9) is one of the factors of  x^2 + mx – 4c = 0  and m and c are positive integers, then which of the following can be a possible value of m x c?

x^2 + mx - 4c = 0
If x+9 is one of the factor, then x=-9 should satisfy the equation.

(-9)^2 -9m - 4c = 0
81 - 9m - 4c = 0
9m + 4c = 81
m = (81-4c)/9 = 9 - 4c/9

(m , c) = {(5,9), (1, 18)}

Possible values of m*c = {45, 18}

IMO E

mysterymanrog · Answer

x^2+mx-4c=0 
we are told that (x+9) is a root, implying that x=-9 gives us 0 in the above equation. 
 (-9)^2-9m-4c=0 
 81-9m-4c=0 
 c=\frac{9(-9+m)}{-4} 
Notice that we are told that c and m are both positive integers. 
As the fraction is divided by a negative number, this places the restriction on the value of m:
(-9+m)<0
0<m<9. 
M must be less than 9 and greater than 0. 
As 4 does not divide 9, (-9+m) must be some multiple of 4. 
The first case is m=1, which gives us c=9*8/4=9*2=18. 
mc in this case would be 18. This is not an option, so there must another case 
The second case is m=5. This gives us c=9*4/4=9
mc=45, which is the option E and is therefore the correct answer.

bumpbot · Answer

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If (x +9) is one of the factors of x2 + mx 4c = 0 and m and c are

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