Find all the zeroes of 2x⁴-3x³-3x²+6x-2
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hence the factors are (x - √2) and (x+ √2) since x=√2 and x= -√2
if you multiply both you'll get x² - 2
when you divide 2x⁴ - 3x³ - 3x² + 6x - 2 by x² - 2 since it is divisible by 2x⁴ - 3x³ - 3x² + 6x - 2
the quotient will turn out to be 2x²- 3x + 1
Now lets factorise this equation,
=>2x² - 3x + 1=0
=>2x² -2x -1x + 1 =0
=>2x(x - 1) -1(x - 1)=0
=>(2x - 1)(x - 1)=0
therefore 2x - 1=0 or x-1=0
which implies x=1/2 or x=1
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