4 x square - 4 x + 1 please
Answers
Answer:
4x²-4x+1
factorisation method
4x²-2x-2x+1 = 0
2x(2x-1)-1(2x-1) = 0
(2x-1)(2x-1) = 0
2x-1=0 2x-1=0
2x=1 2x=1
x=1/2 x=1/2
therefore values of x are 1/2 , 1/2
First Possible Question
Factorize 4x² - 4x + 1
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Answer
We will factorize the above using a special algorithm.
Product (The product of the coefficient without including the square value of the first term and the third term) ⇒ (+4) × (+1) = 4
Sum (The coefficient of the second term) ⇒ -4
Now we have to find two multiples of the product part that when we add or subtract we get the sum part. (Don't concentrate on the negative or positive sign)
Possible Numbers.
⇒ 1 , 4
⇒ 2 , 2
Here,
1 + 4 = 5 ≠ 4
4 - 1 = 3 ≠ 4
2 + 2 = 4 = 4
2 - 2 = 0 ≠ 4
∴ We will split the middle term using the obtained number.
⇒ 4x² - 4x + 1
⇒ 4x² - 2x - 2x + 1
Common factors of first two terms
4x² ⇒ 2 × 2 × x × x
-2x ⇒ -1 × 2 × x
Common Factor ⇒ 2x
⇒ 4x² - 2x - 2x + 1
⇒ 2x (2x - 1) - 2x + 1
Common factors of last two terms.
-2x ⇒ -1 × 2 × x
1 ⇒ -1 × -1
Common factor ⇒ -1
⇒ 2x (2x - 1) - 1 (2x - 1)
⇒ (2x - 1)(2x - 1)
∴ When we factorize 4x² - 4x + 1 we get (2x - 1)(2x - 1).
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Second Possible Question
Find 'x' in the equation ⇒ 4x² - 4x + 1 = 0
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Answer
Let's solve your equation step-by-step.
4x² - 4x + 1 = 0
Step 1: Factor left side of equation.
⇒ 4x² - 2x - 2x + 1
⇒ 2x (2x - 1) - 2x + 1
⇒ 2x (2x - 1) - 1 (2x - 1)
⇒ (2x - 1)(2x - 1)
Step 2: Set factors equal to 0.
⇒ 2x - 1 = 0 or 2x - 1 = 0
⇒ 2x = 1 or 2x = 1
⇒ x = ¹/₂ or x = ¹/₂
∴ The value of 'x' in the given equation is ¹/₂
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