If x^2 - 2x - 15 = 0 and x 0, which of the following must

Question

If x^2 - 2x - 15 = 0 and x > 0, which of the following must be equal to 0 ?

I. x^2 - 6x + 9
II. x^2 -7x + 10
III. x^2 - 10x + 25

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

Bunuel · Accepted Answer

SOLUTION

If x^2 - 2x - 15 = 0 and x > 0, which of the following must be equal to 0 ?

I. x^2 - 6x + 9
II. x^2 -7x + 10
III. x^2 - 10x + 25

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

Factor  x^2 - 2x - 15 = 0  -->  (x-5)(x+3)=0  -->  x=5  or  x=-3 . Since given that x>0, then  x=5  only.

Now, substitute  x=5  into the options to see which one equals to 0. Only II and III give 0.

Answer: D.

Fabino26 · Answer

Remember the formula for second degree equations and solve for x(1) x(2): 
x(1) + x(2) = - (-2)
x(1)*x(2)= -15

x(1) = -3
X(2)= 5

Now given that x>0, x must be equal to 5. 
only II and III include a 5 given the last terms are 10 (II) and 25 (III). Hence, we have to check if they include a positive or negative 5. 
=> The solution for II is 2,  5 . Sufficient
=> The solution for III is  5 ,  5 . Sufficient

Solution: D

AKG1593 · Answer

Ans. D

x^2 -2x - 15=0
x^2 - 5x + 3x -15=0
(x+3)(x-5)=0
x=5 (x=-3 is not possible since x>0)

II and III statements have (x-5) as factors therefore will be '0'.

nutshell · Answer

Solve x^2 - 2x - 15 = 0:
(x-5)(x+3) = 0;
x = -3, 5.

Since x is given as positive(x > 0), x = 5 is the valid one.

Substitute the value of x = 5 in the equations:
I. 25 - 30 + 9 = 4#0; Reject.
II. 25 - 35 + 10 = 0; Correct.
III. 25 - 50 + 25 = 0; Correct.

II and III only.

Ans is (D).

BrentGMATPrepNow · Answer

Given:  x^2-2x-15=0  
Factor:  (x-5)(x+2)=0 
So, either  x = 5  or  x = -3  
Since we're told  x>0 , we know that it must be the case that  x = 5

Now we can plug  x = 5  and to each of the given expressions to see which one(s) evaluate to be zero...

I.  x^2-6x+9 
We get:  5^2-6(5)+9=25-30+9=4

II.  x^2-7x+10 
We get:  5^2-7(5)+10=25-35+10=0

III.  x^2-10x+25 
We get:  5^2-10(5)+25=25-50+25=0

Answer: D

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If x^2 - 2x - 15 = 0 and x > 0, which of the following must

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