Question

verify the zeroes of the polynomial p(x) =x*2-1, x=-1&1​

Answer 1

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Answer

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)

−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 −3

9−1−5−33−27

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

= 39−3−135

= a−bαβ+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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