Carcass wrote:

The function f is defined for all numbers x by f (x) = x² + x. If t is a number such that f (2t) = 30, which two of the following could be the number t ?

Indicate

two such numbers.

❑ —5

❑ —3

❑ \(\frac{1}{2}\)

❑ 2

❑ \(\frac{5}{2}\)

If f(x) = x² + x, then f(2t) = (2t)² + 2t

Since f(2t) = 30, we know that: (2t)² + 2t = 30

Simplify: 4t² + 2t = 30

Subtract 30 from both sides: 4t² + 2t - 30 = 0

Divide both sides by 2 to get: 2t² + t - 15 = 0

Factor to get: (2t - 5)(t + 3) = 0

So, EITHER 2t - 5 = 0 OR t + 3 = 0

If 2t - 5 = 0, then t = 5/2

If t + 3 = 0, then t = -3

Answer:

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Brent Hanneson – Creator of greenlighttestprep.com

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