Two of the zeroes of x^4 - 6x^3 - 26x^2 + 138x - 35 are 2 + √3 and 2 - √3. The product (x - (2 + √3))(x - (2 - √3)) equals which quadratic factor?

Question

Accepted Answer

x^2 - 4x + 1. Sum of roots = 4, product = (2)^2 - (√3)^2 = 4 - 3 = 1. So factor = x^2 - 4x + 1.

Two of the zeroes of $x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35$ are $2 + 3$ and $2 - 3$ .
The product $(x - (2 + 3)) (x - (2 - 3))$ equals which quadratic factor?