Question

if polynomail so x^3+ax^2+5 and x^3-2x^2+a are divide by (x+2) leave same remaider find the value of a​

Answer 1

Answer:

- 13/3

Step-by-step explanation:

Using remainder theorem: if they leave a remainder(say k), then on subtituting a from (x - a), they must leave k on the other side. So here, value to be subtituted inplace of x is -2(from x+2=x-(-2))

=> (-2)³ + a(-2)² + 5 = k, also,

(-2)³ - 2(-2)² + a = k

- + - -

4a + 8 + 5 - a = 0

=> 3a + 13 = 0

=> 3a = -13

=> a = - 13/3

Answer 2

Step-by-step explanation:

Given : -

• if polynomail so x^3+ax^2+5 and x^3-2x^2+a are divide by (x+2 )

To Find : -

• find the value of a

Solution : -

x + 2

x = - 2

• x³ + ax² + 5 .........( 1 )

• x³ - 2x² + a ........... ( 2 )

✪ According to Equ. 1 :✪

➻ x³ + ax² + 5

➻ ( - 2 )³ + a ( -2 )² + 5

➻ -8 + 4a + 5 ........ ( 4 )

☯ According to Equ. 2 :✪

➻ x³ - 2x² + a

➻ ( - 2 )³ - 2 ( - 2)² + a

➻ - 8 - 8 + a ......... ( 5 )

✪ Substract the equ 4 to Equ 5. :✪

- 8 + 4a + 5 = 0

- 8 + a - 8 = 0

+ - +

______________

3a + 13 = 0

➻ 3a = - 13

➻ a = - 13 / 3