Question

If the polynomials x^3+ 2x^2- 5ax -7 and x^3+ ax^2- 12x + 6 are divided by (x+1) and (x-2), the remainders are respectively R1 and R2 , and 2R1 + R2 = 6, then find the value of ‘a’. Please answer fast anybody.

Answer 1

Step-by-step explanation:

• x + 1 = 0

=> x = -1

= x³ - 2x² - 5ax - 7

=> (-1)³ - 2(-1)² - 5a(-1) - 7

=> - 1 - 2 + 5a - 7

=> 5a - 10 _______ (eq 1)

_______________________________

• x - 2 = 0

=> x = 2

= x³ - ax² - 12x + 6

=> (2)³ - a(2)² - 12(2) + 6

=> 8 - 4a - 24 + 6

=> - 4a - 10 ________ (eq 2)

______________________________

• + = 6

=> 2(5a + 10) + (- 4a - 10) = 6

=> 10a + 20 - 4a - 10 = 6

=> 6a + 10 = 6

=> 6a = - 4

_____________________________

a = or

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