Question

Verify −1/ 3 and 3/ 2 are the zeros of p(x)=6x^2 -3-7x.

Answer 1

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)

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

)−3

9

−1

−

9

5

+

3

11

−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

=

3

9−3−1

3

5

=

a

−b

αβ+βγ+γα

=(3)(−1)+(−1)(

3

−1

)+(

3

−1

)(3)

3

−9+1−3

=

3

−11

=

a

c

αβγ

=(3)(−1)(

3

−1

)

1=

a

d

Thus the relation are verified.