find all the zeros of the polynomial 2x4-8x3+5x2+4x-3,whose two zeroes are 1/root2 and - 1/root 2
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Step-by-step explanation:
given two zeroes of p(x)=1/root2 and -1/root2
By factor theorem
(x-1/root2) (x+1/root2)=0
using identity (a-b) (a+b) = a^2-b^2
x^2-(1/root2)^2=0
x^2-1/2=0
2x^2/2-1/2=0
2x-1 =0
by long division method
2x^4-8x^3+5x^2+ 4x-3÷2x^2-1
q(x)=x^2-4x+3
for other 2 zeroes let p(x) =0
therefore, x^2-4x+3=0
by splitting middle terms
x^2-(3+1)x+3=0
x^2-3x-x+3=0
x(x-3)-1(x-3)=0
(x-1) (x-3) =0
either x-1=0 or x-3=0
x=1 or x= 3
therefore, all the zeros of p(x) are 1,3,1/root2 and -1 /root2
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