Obtain all zeroes of the polynomial x4 - 3x3 - x2 + 9x - 6 = 0, if two of its zeroes are √3 and - √3.
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Hii friend,
✓3 and -✓3 are the zeros of the P(X).
(X-✓3) (X+✓3) = X²-(✓3)² => X²-3
P(X) = X⁴-3X³-X²+9X-6
G(X) = X²-3.
On dividing P(X) by G(X) we get,
Remainder = 0
And,
Quotient = X²-3X+2
Factories the Quotient X²-3X+2 then we will get the two other zeros of the P(X).
=> X²-3X+2
=> X²-2X-X+2
=> X(X-2) -1(X-2)
=> (X-2) (X+1)
=> (X-2) = 0 OR (X+1) = 0
=> X = 2 OR X = -1
Therefore,
2 , -1 , ✓3 and -✓3 are the four zerso of the polynomial X⁴-3X³-X²+9X-6 .
HOPE IT WILL HELP YOU..... :-)
✓3 and -✓3 are the zeros of the P(X).
(X-✓3) (X+✓3) = X²-(✓3)² => X²-3
P(X) = X⁴-3X³-X²+9X-6
G(X) = X²-3.
On dividing P(X) by G(X) we get,
Remainder = 0
And,
Quotient = X²-3X+2
Factories the Quotient X²-3X+2 then we will get the two other zeros of the P(X).
=> X²-3X+2
=> X²-2X-X+2
=> X(X-2) -1(X-2)
=> (X-2) (X+1)
=> (X-2) = 0 OR (X+1) = 0
=> X = 2 OR X = -1
Therefore,
2 , -1 , ✓3 and -✓3 are the four zerso of the polynomial X⁴-3X³-X²+9X-6 .
HOPE IT WILL HELP YOU..... :-)
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