If the two zeroes of the polynomial x4 - 6x3 - 26x2 + 138x - 35 are 2 + √3, 2 - √3 find other zeroes.

Given 2 + √3 and 2 – √3 are zeroes of the given polynomial. So, (2 + √3)(2 – √3) is a factor of polynomial.

Therefore,[x – (2 + √3)][x – (2 – √3)] = x² + 4 − 4x − 3 = x² − 4x + 1 is a factor of the given polynomial

For finding the remaining zeroes of the given polynomial, we will find

Clearly, x⁴ -6x³ -26x²+138x -35 = (x² – 4x + 1)(x² – 2x – 35)

We know, (x² – 2x – 35) = (x – 7)(x + 5)

Therefore, the value of the polynomial is also zero when (x -7 = 0) or (x + 5 = 0)

Or x = 7 or −5

therefore, 7 and −5 are also zeroes of this polynomial.