find all zeroes of the polynomial 2x4-2x3-7x2+3x+6 if two of its zeroes are( x-root3/2) and (x+ root3/2)
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f(x) = 2x4 –2x3 – 7x2 + 3x + 6

Now

So, f (x) = 2x4 – 2x3 – 7x2 + 3x + 6
= (2x2 – 3) (x2 – x – 2)
= (2x3 – 3) (x + 1) (x – 2)
Hence the other two zeroes of f (x ) are – 1 and 2.

Now

So, f (x) = 2x4 – 2x3 – 7x2 + 3x + 6
= (2x2 – 3) (x2 – x – 2)
= (2x3 – 3) (x + 1) (x – 2)
Hence the other two zeroes of f (x ) are – 1 and 2.
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