find the square of root of 64x^4-16x^3+17x^2x+1
Answers
Before proceeding to find the square root of a polynomial, one has to ensure that the degrees of the variables are in descending or ascending order.
Step-by-step explanation:
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Therefore the square root of the given polynomial 64x⁴ - 16x³ + 17x² - 2x + 1 is '8x² - x + 1'.
Given:
Polynomial: 64x⁴ - 16x³ + 17x² - 2x + 1 = 0
To Find:
The square root of 64x⁴ - 16x³ + 17x² - 2x + 1 = 0
Solution:
The given question can be answered as shown below.
By dividing as shown below we get,
8x² ) 64x⁴ - 16x³ + 17x² - 2x + 1 ( 8x²
64x⁴
(-)
16x² - x ) - 16x³ + 17x² ( -x
- 16x³ + x²
(-)_
16x² - 2x + 1 ) 16x² - 2x + 1 ( 1
16x² - 2x + 1
(-)
0
Adding the quotients = 8x² - x + 1
⇒ 64x⁴ - 16x³ + 17x² - 2x + 1 = ( 8x² - x + 1 )²
⇒ √ ( 64x⁴ - 16x³ + 17x² - 2x + 1 ) = √ ( ( 8x² - x + 1 )² = 8x² - x + 1
Therefore the square root of the given polynomial 64x⁴ - 16x³ + 17x² - 2x + 1 is '8x² - x + 1'.
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