Question

If the two zeroes of the polynomial x4
– 8x3
+ 20x2
– 20x + 7 are 3 ±√2, find other

zeroes​

Answer 1

Step-by-step explanation:

If two zeroes of the polynomial x^4 - 6x^3 - 26x^2 + 138x - 35 are 2±√(3) , find the other zeroes.

The two zeroes of the polynomial is 2 + √(3), 2 - √(3) Therefore, (x - 2 + √(3))(x - 2 - √(3)) = x^2 + 4 - 4x - 3 = x^2 - 4x + 1 is a factor of the given polynomial.

Using division algorithm, we get x^4 - 6x^3 - 26x^2 + 138x - 35 = (x^2 - 4x + 1)(x^2 - 2x - 35)

So, (x^2 - 2x - 35) is also a factor of the given polynomial. x^2 - 2x - 35 = x^2 - 7x + 5x - 35 = x(x - 7) + 5(x - 7) = (x - 7)(x + 5)

Hence, 7 and - 5 are the other zeros of this polynomial.