If root 3 and minus( - )root 3 are the zeroes of x^4- x^3- 5x^2+3x + 36 then find all other zeroes.
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If root 3 and minus( - )root 3 are the zeroes of x^4- x^3- 5x^2+3x + 36 then find all other zeroes.
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Answer:
P(X) x⁴+x³-9x²-3x+18
Zeros are: √3, -√3
Factor of zeros are ( x-√3 ), ( X+√3 )
(X)²- (√3)²
X²-3 is a factor
: Division:
X²-3) x⁴+x³-9x²-3x+18( x²+x-6
X²+0x-3x
_______
X³-6x-3x+18
X³+0x-3x
________
-6x²+18
-6x²+18
______
0
_______
Remainder is : x²+x-6
X²+x-6( middle term spitting )
X²+x-6
X²-2x+3x-6
X(x-2)3(x-2)
(X+3)(x-2)
X+3=0, x-2=0
X=-3, X=2
Other zeros are 2,-3