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Consider the function f(x) = x^2 – 5x. For which value(s) of x does

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Bunuel
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Consider the function f(x) = x^2 – 5x. For which value(s) of x does [#permalink] New post   22 Jul 2019, 01:06
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Consider the function \(f(x) = x^2 – 5x\). For which value(s) of x does \(f(x) = 14\)?

I. 7
II. 2
III. –2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III
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D
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Re: Consider the function f(x) = x^2 – 5x. For which value(s) of x does [#permalink] New post   22 Jul 2019, 02:53
Bunuel wrote:
Consider the function \(f(x) = x^2 – 5x\). For which value(s) of x does \(f(x) = 14\)?

I. 7
II. 2
III. –2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III



Given: Consider the function \(f(x) = x^2 – 5x\).
Asked: For which value(s) of x does \(f(x) = 14\)?

I. 7
\(f(x) = x^2 – 5x = 7^2 = 5*7 = 49 -35 = 14\) Correct
II. 2
\(f(x) = x^2 – 5x = 2^2 - 2*5 = 4- 10 = -6 <>14\) Incorrect
III. –2
\(f(x) = x^2 – 5x = (-2)^2 - 5 (-2) = 4+10=14\) Correct

IMO D
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Mohammadmo
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Re: Consider the function f(x) = x^2 – 5x. For which value(s) of x does [#permalink] New post   22 Jul 2019, 02:55
Let put the numbers in the formula so we've got:
7^2 -5×(7)=14 ✔
2^2 -5×(2)=-6 ✖
(-2)^2-5×(-2)=14✔
Option( D)

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Re: Consider the function f(x) = x^2 – 5x. For which value(s) of x does [#permalink] New post   30 Jul 2019, 09:48
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Bunuel wrote:
Consider the function \(f(x) = x^2 – 5x\). For which value(s) of x does \(f(x) = 14\)?

I. 7
II. 2
III. –2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


Let’s plug in each answer choice:

7^2 - 5(7) = 49 - 35 = 14

I works.

2^2 - 5(2) = 4 - 10 = -6

II does not work.

(-2)^2 - 5(-2) = 4 + 10 = 14

III works.

Alternate Solution:

We can set the function equal to 14 and solve:

x^2 - 5x = 14

x^2 -5x - 14 = 0

(x - 7)(x + 2) = 0

x = 7 or x = -2

Thus, statements I and III are solutions.

Answer: D
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Consider the function f(x) = x^2 – 5x. For which value(s) of x does [#permalink] New post   06 Jan 2022, 11:47
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Given that \(f(x) = x^2 – 5x\) and we need to find those values of x for which \(f(x) = 14\)

f(x) = 14
=> \(x^2 – 5x = 14\)
=> \( x^2 - 5x - 14 = 0\)
=> \( x^2 - 7x + 2x - 14 = 0\)
=> x(x-7) +2(x-7) = 0
=> (x-7)*(x+2) = 0
=> x = -2, 7 => I and III

So, Answer will be D
Hope it helps!

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Consider the function f(x) = x^2 – 5x. For which value(s) of x does [#permalink]
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