Find all rational zeros of P(x) = x3 - 7x + 6

Zeros are  

x

=

−

1

,

x

=

−

2

and

x

=

3

Explanation:

f

(

x

)

=

x

3

−

7

x

−

6

;

By inspection  

f

(

−

1

)

=

0

,so

(

x

+

1

)

will be a factor.

x

3

−

7

x

−

6

=

x

3

+

x

2

−

x

2

−

x

−

6

x

−

6

=

x

2

(

x

+

1

)

−

x

(

x

+

1

)

−

6

(

x

+

1

)

=

(

x

+

1

)

(

x

2

−

x

−

6

)

=

(

x

+

1

)

(

x

2

−

3

x

+

2

x

−

6

)

=

(

x

+

1

)

{

x

(

x

−

3

)

+

2

(

x

−

3

)

}

∴

f

(

x

)

=

(

x

+

1

)

(

x

−

3

)

(

x

+

2

)

∴

f

(

x

)

will be zero

for  

x

=

−

1

,

x

=

−

2

and

x

=

3

Hence zeros are  

x

=

−

1

,

x

=

−

2

and

x

=

3

[Ans]

Step-by-step explanation:

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