Question

find a if the two polynomials ax^3 + 3x^2 - 9 and 2x^3 + 4x +a leaves same remaidr when divided by (x + 3)?

Answer 1

Answer:

• Value of a is 3.

Step-by-step explanation:

Given :

• f(x) = ax³ + 3x² - 9.
• g(x) = 2x³ + 4x + a.
• [÷ (x + 3), remainder = -3]

Now, f(-3) :

⇒ a(-3)³ + 3(-3)² - 9

⇒ a(-27) + 3(9) - 9

⇒ -27a + 27 - 9

∴ -27a + 18

Now, g(-3) :

⇒ 2(-3)³ + 4(-3) + a

⇒ 2(-27) + 4(-3) + a

⇒ -54 - 12 + a

∴ -66 + a

Now, f(-3) = g(-3) :

⇒ -27a + 18 = -66 + a

⇒ -27a - a = -66 - 18

⇒ -28a = -84

⇒ a = -84/-28

∴ a = 3

Answer 2

Given :-

ax³ + 3x² - 9

2x³ + 4x + a

To Find :-

Value of a

Solution :-

x + 3 = 0

x = 0 - 3

x = -3

Putting x = -3 in 1

a(-3)³ + 3(-3)² - 9

a(-27) + 3(9) - 9

-27a  + 27 - 9

-27a + 18 (1)

Putting x = -3 in 2

2(-3)³ + 4(-3) + a

2(-27) + (-12) + a

-54 - 12 + a

-66 + a (2)

On comparing

-66 + a = -27a + 18

-66 - 18 = -27a - a

-84 = -28a

a = -84/-28

a = 3