find all the zeros of 2x^4 - 9x^3 + 5x^2 + 3x - 1 if two of its zeros are 2+√3 and 2-√3
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(2+√3) and (2-√3) are the 0's of the polynomial
⇒ [x - (2+√3)] and [x - (2-√3)] are the factors
[x - (2+√3)] [x - (2-√3)] = x2 - 4x + 1
(2x⁴ - 9x³ + 5x² + 3x - 1) ÷ (x² - 4x + 1)
= (2x₂ - x - 1)
=(2x² - x - 1)
=2x²-2x+x-1
=2x(x-1)+1(x-1)
=(2x+1)(x-1)
∴ The the other two 0's are -1/2 and 1 .
⇒ [x - (2+√3)] and [x - (2-√3)] are the factors
[x - (2+√3)] [x - (2-√3)] = x2 - 4x + 1
(2x⁴ - 9x³ + 5x² + 3x - 1) ÷ (x² - 4x + 1)
= (2x₂ - x - 1)
=(2x² - x - 1)
=2x²-2x+x-1
=2x(x-1)+1(x-1)
=(2x+1)(x-1)
∴ The the other two 0's are -1/2 and 1 .
Lipimishra2:
Wrong a bit
When you factorize 2x^2-x-1,
The answer will be (2x+1)(x-1)
Zeroes are -1/2 and 1
CORRECT IT NOW!
did..thanks for rectifying :-)
Nvm. ^_^
thanks lipimishra
Aw. ^_^
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