Question

if two zeros of the polynomial 3x^3-x^2-3x+1, is 1 then find all the other zeros​

Answer 1

Answer:

Correct option is

D

−1 and

3

1

Let α,β be the zeros of the cubic polynomial

3x

3

−x

2

−3x+1.

1+α+β=−

coefficient of x

3

coefficient of x

2

=

3

−(−1)

=

3

1

⇒α+β=

3

1

−1=

3

(−2)

(i)

Also,

1×α×β=−

a

d

=−

coefficient of x

3

constant term

αβ=−

3

1

⇒α=−

3β

1

Putting the value α=−

3β

1

in equation (i)

⇒

3β

−1

+β=−

3

2

⇒

3β

−1+3β

2

=−

3

2

⇒−1+3β

2

=−2β

⇒3β

2

+2β−1=0

⇒3β

2

+3β−β−1=0

⇒3β(β+1)−1(β+1)=0

⇒(β+1)(3β−1)=0

β=−1,β=

3

1

Now,

⇒α=−

3β

1

Putting the value of β

⇒α=−

3(−1)

1

=

3

1

or,

α=−

3(

3

1

)

1

=−1

Therefore, α,β=(

3

1

,−1)or(−1,

3

1

)

Hence, option D is correct.