Math, asked by sanikanaik32680, 3 months ago

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

Answers

Answered by skpillai636
2

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=−

1

Putting the value α=−

1

in equation (i)

−1

+β=−

3

2

−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=−

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

)

Answered by deepak1463
1

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.

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