Question

find all the zeroes of the polynomial x^4-3x^3+6x-4, if two of its zeroes are √2 and -√2.
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Answer 1

Given: root 2 and- root 2 are zeroes.
So, (x-r 2)(x+r2)
=》x square - 2

Now divide the p(x) by this

s - squqre and r- root

xs -3x +2
___________ xs- 2_/x^4-3x^3+6x-4\_
- x^4 -2x^2
+_________________-3x^3+2x^2+6x-4
-3x^3 +6x
+_________-_____
2x^2-4
2x^2 -4
-_______+___
0
______


Now,
=》x^2-3x+2
=》x^2-2x-x+2
=》x (x-2)+1 (x-2)
=》(x+1)and(x-2)
For zeroes
x+1=0 and x-2=0
so x= (-1) and (2)

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