Question

if 1 Of The zeros Of The polynomial 3xsq -10x + p is 1/3​

Answer 1

Answer:

Step-by-step explanation:

Answer

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

​

)

Answer 2

Step-by-step explanation:

The first person to document zero as a number in its own right was the astronomer and mathematician Brahmagupta in 628 CE.