Find all zeroes of polynomial 4x4-20x3+23x2+5x-6 if two of its zeroes are 2 and 3
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2 and 3 are the zero of polynomial.
then x= 2 also x= 3
(x-2) (x-3) is a factor of this polynomial
(x-2) (x-3)= x^2-5x+6.
Divide the polynomial by the factor we get : 4x^4 - 20x^3 +23x^2 +5x-6 / x^2 -5x +6.
Q(x) = 4x^2 - 1 .
Factorize 4x^2 - 1 we get : (2x ) ^2 - (1)^2 .
= (2x+1) (2x-1).
= 2x+1 =0 , x= -1/2 .
= 2x - 1 =0 , x = 1/2 .
it's other two zero are -1/2 , 1/2 .
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