Obtain all zeros of the polynomial f x is equal to X 4 - 3 x cube minus x square + 9 x minus 6 . If two of its zeros are minus under root 3 and under 3.
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Hiii friend,
✓3 and -✓3 are the factor of P(X)
(X-✓3)(X+✓3) = (X)²-(✓3)² = X²-3
G(X) = X²-3X
P(X) = X⁴-3X³-X²+9X-6
On dividing P(X) by G(X) we get,
REMAINDER = 0
QUOTIENT = X²-3X+2
Factories the Quotient then we will get the two other zeros of the Polynomial X⁴-3X³-X²+9X-6.
X²-3X-2
=> X²-2X-X+2
=> X(X-2) -1(X-2)
=> (X-2)(X-1)
=>(X-1)= 0 (X-2) = 0
=> X = 1 OR X = 2
Hence,
1 , 2 , ✓3 and -✓3 are the four zeros of P(X).
HOPE IT WILL HELP YOU...... :-)
✓3 and -✓3 are the factor of P(X)
(X-✓3)(X+✓3) = (X)²-(✓3)² = X²-3
G(X) = X²-3X
P(X) = X⁴-3X³-X²+9X-6
On dividing P(X) by G(X) we get,
REMAINDER = 0
QUOTIENT = X²-3X+2
Factories the Quotient then we will get the two other zeros of the Polynomial X⁴-3X³-X²+9X-6.
X²-3X-2
=> X²-2X-X+2
=> X(X-2) -1(X-2)
=> (X-2)(X-1)
=>(X-1)= 0 (X-2) = 0
=> X = 1 OR X = 2
Hence,
1 , 2 , ✓3 and -✓3 are the four zeros of P(X).
HOPE IT WILL HELP YOU...... :-)
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