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

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Bunuel
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If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   03 Feb 2014, 01:16
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A
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D
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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
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D
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   03 Feb 2014, 01:16
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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.
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   03 Feb 2014, 02:04
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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
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   03 Feb 2014, 11:23
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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'.
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   04 Feb 2014, 01:49
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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).
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must be equal [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   30 Sep 2021, 06:53
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Bunuel
If \(x^2-2x-15=0\) and \(x>0\), which of the following must be equal to zero ?

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

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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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] If x^2 - 2x - 15 = 0 and x > 0, which of the following must   13 Jun 2023, 07:12
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink]
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