Question

List all potential rational zeros of 9x^3+6x^2-29x-10

Answer 1

9 x ^ 3 + 6 x ^ 2 - 29 x - 10

Since the constant in the given equation is a 10 , we know that the integer root must be a factor of 10.

The possible values are :

+ OR - 1

+ OR -2

+ OR - 5

and

+ OR - 10


You can use the factor theorem to test the possible values by trial and error :


f ( 1 ) = 9 + 6 - 29 - 10 = -24 ¡Ù 0

f ( ¨C 1 ) = ¨C 9 + 6 + 29 ¨C 10 = 16 ¡Ù 0


f ( 2 ) = 72 + 24 ¨C 58 ¨C 10 = 28 ¡Ù 0

f ( - 2 ) = - 72 + 24 + 58 ¨C 10 = 0


f ( 5 ) = 1125 + 150 ¨C 145 ¨C 10 = 1120 ¡Ù 0

f ( - 5 ) = - 1125 + 150 + 145 ¨C 10 = - 840 ¡Ù 0


f ( 10 ) = 9000 + 600 ¨C 290 ¨C 10 = 9300 ¡Ù 0

f ( - 10 ) = - 9000 + 600 + 290 ¨C 10 = - 8120 ¡Ù 0


The integer root is - 2


Divide 9 x ^ 3 + 6 x ^ 2 - 29 x - 10 with [ x - ( - 2 ) ]

x - ( - 2 ) = x + 2 so :


( 9 x ^ 3 + 6 x ^ 2 - 29 x - 10 ) / ( x + 2 ) =

9 x ^ 2 - 12 x - 5

Now :

9 x ^ 3 + 6 x ^ 2 - 29 x - 10 =

( x + 2 ) ( 9 x ^ 2 - 12 x - 5 )


Now in google type:

quadratic equation online

When you see list of results click on:

Free Online Quadratic Equation Solver:Solve by Quadratic Formula

When page be open click option :

Solve by Factoring (includes Factoring by Grouping)

then in rectangle type :

9 x ^ 2 - 12 x - 5 = 0

and click optin: solve it!

You will see solution step by step


So solution of your equations are :

x = - 2

x = - 1 / 3

and

x = 5 / 3

________________________________________

P.S.

If you don't know how to divide 9 x ^ 3 + 6 x ^ 2 - 29 x - 10 with x + 2

go on :

calc101 dot com

When page be open click option :

long division

Then in up rectangle type :

9 x ^ 3 + 6 x ^ 2 - 29 x - 10

In down rectangle type :

x + 2

and click option :

DO IT
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Answer 2

¡Ù

mean :

different of

f ( ¨C 1 ) = ¨C 9 + 6 + 29 ¨C 10 = 16 ¡Ù 0

mean :

f ( - 1 = 16 differen of 0