Question

Find the zero of polynomial 3x2 - 1 1x -34 and verify the relationship between zero and coefficient of Polynomial. ​

Answer 1

Step-by-step explanation:

We have,

p(x)=3x 3 −5x 2 −11x−3

And the zeros are

3,−1,

3−1

Verifying the zeros,

x=3,p(3)=3(3)

3

−5(3)

2

−11(3)−3

=81−45−33−3

=0

=x−1,p(−1)=3(−1)

3

−5(−1)

2

−11(−1)−3

=−3−5+11−3

=0

x= 3−1,p( 3−1 )=3( 3−1 )

3 −5( 3−1 ) 2 −11( 3−1 )−39−1 − 95

+ 311 −39−1−5−33−27

0

Now verifying the relation between zeros and coefficients is:

for,

p(x)=3x

3 −5x 2 −11x−3

a=3,b=−1,c=−11,d=−1

and zeros α=3,β=−1γ= 3−1

Now,

α+β+γ

=3+(−1)+ 3−1

= 39−3−1

35 = a−b

αβ+βγ+γα

=(3)(−1)+(−1)( 3−1 )+( 3−1 )(3)3−9+1−3

= 3−11 = ac

αβγ

=(3)(−1)( 3−1 )

1= ad

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