Question

If 2+√3 is a root of 6x-13x³-35x²-x+3=0 then​

Answer 1

Step-by-step explanation:

The equation 6x

4

−13x

3

−35x

2

−x+3=0 has all rational coefficients.

As 2+

3

is a root, its conjugate 2−

3

is also a root of the equation in order to have rational coefficients.

Hence, (x−(2+

3

))(x−(2−

3

)) is a factor of the equation.

⇒(x

2

−4x+1) is a factor of 6x

4

−13x

3

−35x

2

−x+3=0

⇒6x

4

−13x

3

−35x

2

−x+3=(x

2

−4x+1)(ax

2

+bx+c)

On comparing the coefficients, we get

a=6,b=11,c=3

Hence, 6x

4

−13x

3

−35x

2

−x+3=(x

2

−4x+1)(6x

2

+11x+3)

⇒6x

4

−13x

3

−35x

2

−x+3=(x

2

−4x+1)(2x+3)(3x+1)

Hence the roots are