2x³ - 9x² + 2 = 0
Steps to solving will be helpful, thanks.
Steps to solving will be helpful, thanks.
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2x³ - 9x² + 2 = 0
=> 2x³ - x² - 8x² + 4x - 4x + 2 = 0
=> x² (2x - 1) - 4x (2x - 1) - 2 (2x - 1) = 0
=> (2x - 1) (x^2 - 4x - 2) = 0.
Can't be factorized further with rational coefficients as the discriminant of the quadratic factor is an irrational number.
Edit:
I read the additional details. The solution is as under.
2x - 1 = 0 or x^2 - 4x - 2 = 0
=> x = 1/2
OR
x
= (1/2) [4 ± √(16 + 8)]
= 2 ± √6.
=> 2x³ - x² - 8x² + 4x - 4x + 2 = 0
=> x² (2x - 1) - 4x (2x - 1) - 2 (2x - 1) = 0
=> (2x - 1) (x^2 - 4x - 2) = 0.
Can't be factorized further with rational coefficients as the discriminant of the quadratic factor is an irrational number.
Edit:
I read the additional details. The solution is as under.
2x - 1 = 0 or x^2 - 4x - 2 = 0
=> x = 1/2
OR
x
= (1/2) [4 ± √(16 + 8)]
= 2 ± √6.
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This polynomial does not have real factors.
;-))
;-))
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(2x – 1)(x² – 4x – 2)