Question

two zeroes of cubic polynomial ax3+3x2-bx-6 are - 1 and - 2. find the other zeroes also.​

Answer 1

Answer:

As x=- 1 x=-2 are zeroes of the polynomial So,

On putting x=-1 in the equation

a(-1)^3 +3(-1)^2-b(-1)-6=0

-a+3+b-6=0

On simplifying,

b-a=3

On putting x=-2 in the equation

a(-2)^3+3(-2)^2-b(-2)-6=0

-8a+12+2b-6=0

On simplifying,

4a-b=3

On solving the 2 equations we get,

a=2

b=5Ans.

Hope this answer helps you.

Answer 2

$\huge {\underline {\underline {\mathtt {\blue{Answer:}}}}}(◍•ᴗ•◍)$

Heya..!!!

ax³ + 3x² - bx - 6

x = -1 , -2

put the values of x in Equation

we get,

a(-1)³ + 3(-1)² - b(-1) - 6 = 0

=> -a + 3 + b - 6 = 0

=> b - a = 3--------(1)

now x = - 2

a(- 2)³ + 3(-2)² - b(-2) - 6 = 0

=> -8a + 12 + 2b - 6 = 0

=> 2b - 8a + 6 = 0

=> b - 4a = -3--------(2)

from--(1) and -----(2)

b - a = 3

b - 4a = -3

(-)___(+)__(+)

___________

3a = 6

=> a = 2 put in --(1)

b - 3 = 2

=> b = 5 now put this value in Equation

ax³ + 3x² - bx - 6 = 0

=> 2x³ + 3x² - 5x - 6 = 0

two zeroes are given (-1 , -2)

(x + 1)(x + 2) = x² + 2x + x + 2 = 0

=> x² + 3x + 2 =0

x² + 3x + 2)2x³ + 3x² - 5x - 6(2x - 3

2x³ + 6x² + 4x

- - -

—————————

-3x² - 9x - 6

-3x² - 9x - 6

+ + +

—————————

0 0 0

hence another zeroes is

2x - 3 = 0

=> x = 3/2

__________________________

Hope It Helps You ✌️