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The function f is defined for all numbers x by f(x) = x^2 + x. If t is 27 May 2019, 02:47
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D
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The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

I. \(- 5\)

II. \(- 3\)

III. \(\frac{5}{2}\)


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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The function f is defined for all numbers x by f(x) = x^2 + x. If t is 27 May 2019, 03:06
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Bunuel
The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

❑ \(- 5\)

❑ \(- 3\)

❑ \(\frac{5}{2}\)

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
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Put the values of t to check,

t= -5
f(-10)= (-10)(-10+1)= 90 Not possible.

t= -3
f(-6) = (-6)(-5)= 30 Possible

t= 5/2
t(5)= 5*6= 30 Possible. D. II and III only
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The function f is defined for all numbers x by f(x) = x^2 + x. If t is 27 May 2019, 03:22
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Bunuel
The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

❑ \(- 5\)

❑ \(- 3\)

❑ \(\frac{5}{2}\)

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
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Substitute 2t in place of x to get \(4t^2\)+2t-30=0 / div by 2, to get
\(2t^2\)-t-15=0
(x-2.5)(x+3). Answer is D (II and III can be true)
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The function f is defined for all numbers x by f(x) = x^2 + x. If t is 27 May 2019, 06:29
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expression of function can be written as
\(f(x) = x^2 + x\)
30= 4t^2+2t
or say
2t^2+t-15=0
2t^2+6t-5t-15=0
2t(t+3)-5(t+3)=0
t=-3 and 5/2
IMO D

Bunuel
The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

I. \(- 5\)

II. \(- 3\)

III. \(\frac{5}{2}\)


A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
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The function f is defined for all numbers x by f(x) = x^2 + x. If t is 28 May 2019, 17:46
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Bunuel
The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

I. \(- 5\)

II. \(- 3\)

III. \(\frac{5}{2}\)


A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
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We can substitute the answer choices:

I. 2(-5) = -10; thus:

f(-10) = 100 - 10 = 90

I is not true.

II. 2(-3) = -6

f(-6) = 36 - 6 = 30

II is true.

III. 2(5/2) = 5

f(5) = 25 + 5 = 30

III is true.

Answer: D
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The function f is defined for all numbers x by f(x) = x^2 + x. If t is 15 Dec 2021, 09:48
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Given that \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\) and t is a number such that \(f(2t) = 30\). And we need to find values of t

Let's start by finding the value of f(2t)
To find f(2t) we need to substitute x = 2t in \(f(x) = x^2 + x\)

=> f(2t) = \((2t)^2 + 2t\) = \(4t^2 + 2t\) = 30 (given)
=> \(4t^2 + 2t - 30 = 0\)

Divide both the sides by 2 we get
=> \(2t^2 + t - 15 = 0\)
=> \(2t^2 + 6t - 5t - 15 = 0\)
=> \(2t(t + 3 ) - 5(t + 3) = 0\)
=> (t + 3) * (2t - 5) = 0
=> t = -3 or t = \(\frac{5}{2}\)
=> II and III

So, Answer will be D
Hope it helps!

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