Question

if two zeroes of the polynomial x^3-6x^2+138x-35 are 2+√3 find other zeroes.​

Answer 1

Step-by-step explanation:

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 −5are the other zeros of this polynomial.

solution

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