Question

If two zeros of the polynomial f(x) = x4−6x3−26x2+138x−35 are 2±√3, find other zeros.

Answer 1

Let the other two zeros be X and Y.

We know that sum of zeroes is 6 by looking at the given polynomial.

X + Y + 4( "sum of 2+-√3" )= 6
X + Y = 2

The product of the zeros by looking at the equation we know is -35.

X×Y×(2+✓3)×(2-✓3) = -35
X×Y = -35

But X + Y = 2

Thus X and Y are 7 and -5.
Thus the other two zeroes are:
7 and -5