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26 May 2021, 01:30
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C
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Difficulty:
55%
(hard)
Question Stats:
59% (01:47) correct
41%
(02:22)
wrong
based on 73
sessions
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If \(x^2 + 12x − k = 0\), is \(x = 4\)?
(1) \((x + 16)\) is a factor of \(x^2 + 12x − k=0\), where k is a constant, and x is a variable.
(2) \(x ≠ −16\)
(1) \((x + 16)\) is a factor of \(x^2 + 12x − k=0\), where k is a constant, and x is a variable.
(2) \(x ≠ −16\)
27 May 2021, 01:15
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If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out \(x+16\) from \(x^2+12x-k=0\), so we would have \((x+16)*(something)=0\). Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):
\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).
Thus according to the above \(x_1+x_2=-16+x_2=\frac{-12}{1}\) --> \(x_2=4\).
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out \(x+16\) from \(x^2+12x-k=0\), so we would have \((x+16)*(something)=0\). Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):
\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).
Thus according to the above \(x_1+x_2=-16+x_2=\frac{-12}{1}\) --> \(x_2=4\).
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
26 May 2021, 03:41
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(1) Let's us know that (x+16) is one factor, and thus (x-4) is the other. In this case x = -16 or x = 4 INSUFFICIENT
(2) Just says that x is not 16, but nothing else. INSUFFICIENT
(1+2) As we know x = -16 or x = 4 from (1), (2) allows us to eliminate -16 and leaves us only with x = 4 SUFFICIENT
Answer C
(2) Just says that x is not 16, but nothing else. INSUFFICIENT
(1+2) As we know x = -16 or x = 4 from (1), (2) allows us to eliminate -16 and leaves us only with x = 4 SUFFICIENT
Answer C
