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# The number of real roots of the equation $2^{2x^{2}-7x+5}=1$ is

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Manager
Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
The number of real roots of the equation $2^{2x^{2}-7x+5}=1$ is  [#permalink]

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11 Feb 2019, 22:16
2
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:25) correct 32% (01:15) wrong based on 34 sessions

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The number of real roots of the equation $$2^{2x^{2}-7x+5}=1$$ is
A) 0
B) 1
C) 2
D) 3
E) 4

Source : Ignus

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NUS School Moderator
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
The number of real roots of the equation $2^{2x^{2}-7x+5}=1$ is  [#permalink]

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11 Feb 2019, 22:25
2
If $$2^{something} = 1$$, then something = 0.

$$2x^2-7x+5 = 0$$
$$2x^2-2x-5x+5 = 0$$
$$2x(x-1)-5(x-1) = 0$$
x = 1 or x = 5/2 = 2.5

2 real roots.

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The number of real roots of the equation $2^{2x^{2}-7x+5}=1$ is   [#permalink] 11 Feb 2019, 22:25
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