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# How many different values of x does the solution set for the equation

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Senior RC Moderator
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How many different values of x does the solution set for the equation  [#permalink]

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21 Mar 2020, 22:05
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Difficulty:

45% (medium)

Question Stats:

55% (01:14) correct 45% (01:13) wrong based on 20 sessions

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How many different values of $$x$$ does the solution set for the equation $$4x^2 = 4x - 1$$ contain?

(A) None
(B) One
(C) Two
(D) Four
(E) Infinitely many

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Posts: 3318
Re: How many different values of x does the solution set for the equation  [#permalink]

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22 Mar 2020, 06:20
2

Solution

Given
In this question, we are given that
• An equation $$4x^2 = 4x – 1$$

To find
We need to determine
• The number of different values of x that satisfy the given equation

Approach and Working out
Solving the given equation, we get:
• $$4x^2 = 4x – 1$$
Or, $$4x^2 – 4x + 1 = 0$$
Or, $$4x^2 – 2x – 2x + 1 = 0$$
Or, $$2x (2x – 1) – 1 (2x – 1) = 0$$
Or, $$(2x – 1) (2x – 1) = 0$$
Or, $$(2x – 1)^2 = 0$$
Hence, $$x = \frac{1}{2}$$

Thus, option B is the correct answer.

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How many different values of x does the solution set for the equation  [#permalink]

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25 Mar 2020, 09:32
We can use the discriminant for solve this question.

Discriminant = (-4)^2 - 4 x(4)x(1) = 16 - 16 = 0
The equation has a unique solution.

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Joined: 23 Mar 2020
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How many different values of x does the solution set for the equation  [#permalink]

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25 Mar 2020, 20:22
How many different values of $$x$$ does the solution set for the equation $$4x^2 = 4x - 1$$ contain?

(A) None
(B) One
(C) Two
(D) Four
(E) Infinitely many

The equation can be rewritten as 0 = 4x^2 - 4x + 1. That equation can be factored into 0 = (2x-1)(2x-1). There is only one x value that can satisfy the equation and thus the answer is (B).
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Re: How many different values of x does the solution set for the equation  [#permalink]

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25 Mar 2020, 21:13
Rearrange the terms : 4x^2–4x+1=0

Upon looking closely we can see that the above equation is expansion of (2x–1)2=0
This equation has only one solution
x=1/2
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Re: How many different values of x does the solution set for the equation   [#permalink] 25 Mar 2020, 21:13
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