Question
Obtain all zeros of the polynomial
2y^3-4y-y^2+2,
if two of its zeroes are 2 and - 2
2y^3-4y-y^2+2,
if two of its zeroes are 2 and - 2
Answers
The zeros of this polynomial are not 2 and - 2.
Write a polynomial in this form:
( 2 y³ - y² ) + ( - 4 y + 2 )
Now factorize the polynomial.
( 2 y³ - y² ) + ( - 4 y + 2 ) =
y² ( 2 y - 1 ) - 2 ( 2 y - 1 ) =
( 2 y - 1 ) ( y² - 2 )
2 y³ - 4 y - y² + 2 = 0
is same as:
( 2 y - 1 ) + ( y² - 2 ) = 0
The solutions are:
2 y - 1 = 0
2 y = 1
y = 1 / 2
and
y² - 2 = 0
y² = 2
y = ± √2
Write a polynomial in this form:
( 2 y³ - y² ) + ( - 4 y + 2 )
Now factorize the polynomial.
( 2 y³ - y² ) + ( - 4 y + 2 ) =
y² ( 2 y - 1 ) - 2 ( 2 y - 1 ) =
( 2 y - 1 ) ( y² - 2 )
2 y³ - 4 y - y² + 2 = 0
is same as:
( 2 y - 1 ) + ( y² - 2 ) = 0
The solutions are:
2 y - 1 = 0
2 y = 1
y = 1 / 2
and
y² - 2 = 0
y² = 2
y = ± √2
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