Question

If two zeroes of the polynomial g(y) = y4 -
6y-26y2+138y-35 are 2+ √3 and 2- √3​

Answer 1

Answer:

The two zeroes of the polynomial is 2+√3​,2−√3

​

∴  (x−2+3​)(x−2−3​)

= x²+4−4x−3

= x²−4x+1 is a factor of the given polynomial.

Using division algorithm, we get

x^4 − 6x³ −26x² + 138x − 35=(x²−4x+1)(x²−2x−35)

So, (x²−2x−35) is also a factor of the given polynomial.

x²−2x−35 = x²−7x+5x−35

= x(x−7) + 5(x−7)

= (x−7)(x+5)

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