Find all zeroes of the polynomial (2x4 - 9x3 + 5x2 + 3x-1) if two of its zeroes are ( 2 + √3 ) and ( 2 - √3 ).
It is given that ( 2 + √3 ) and ( 2 - √3 ) are two zeros of 2x4 - 9x3 + 5x2 + 3x-1
Let us now divide f(x) by x2-4x + 1
therefore, we have,
f(x) = (x2- 4x + 1)(2x2-x-1)
Hence, other two zeros of f(x) are the zeros of the polynomial 2x2-x-1
We have,
2x2-x-1 = 2x2- 2x+ x-1
= 2x (x-1) + 1(x-1)
= (2x+ 1)(x-1)
Hence, the other two zeros are - 1/2 and 1.