Math, asked by thakurdhruvpratap742, 18 days ago

W 2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two time, and the product of its zeroes as 2.-7, -14 respectively. These exercises are not from the examination point of view?​

Answers

Answered by AbhinavJoemon
0

Answer: Let p(x)=x  

3

+3x  

2

−x−3

p(1)=(1)  

3

+3(1)  

2

−1−3=0

p(−1)=(−1)  

3

+3(−1)  

2

+1−3=0

p(−3)=(−3)  

3

+3(−3)  

2

+3−3=0

Hence, 1,−1 and −3 are the zeroes of the given polynomial.

If α,β,γ, are roots of a cubic equation  ax  

3

+bx  

2

+cx+d=0, then

1.   α+β+γ=−  

a

b

 

2.  α×β+γ×β×γ+α×γ=  

a

c

 

3.   α×β×γ=−  

a

d

 

⇒−3=−  

a

b

 

−3=−  

1

3

=−3

⇒−1=−  

1

1

 

−1=−1

⇒3=−  

1

(−3)

 

3=3

Hence the relationship between zeroes and coefficients is also satisfied.

Let p(x)=x  

3

+3x  

2

−x−3

p(1)=(1)  

3

+3(1)  

2

−1−3=0

p(−1)=(−1)  

3

+3(−1)  

2

+1−3=0

p(−3)=(−3)  

3

+3(−3)  

2

+3−3=0

Hence, 1,−1 and −3 are the zeroes of the given polynomial.

If α,β,γ, are roots of a cubic equation  ax  

3

+bx  

2

+cx+d=0, then

1.   α+β+γ=−  

a

b

 

2.  α×β+γ×β×γ+α×γ=  

a

c

 

3.   α×β×γ=−  

a

d

 

⇒−3=−  

a

b

 

−3=−  

1

3

=−3

⇒−1=−  

1

1

 

−1=−1

⇒3=−  

1

(−3)

 

3=3

Hence the relationship between zeroes and coefficients is also satisfied.

Step-by-step explanation:

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