Question

Let R1 and R2 be the remainders when f(x)=x^3+2x^2-5ax-7 and g(x)=2x^3+ax^2-6x+2are divided by (x+1)and (x+2) respectively.If 2R1+R2=0.Find the value of a............. QUICK!!!!!!!!!

Answer 1

Answer:

a = 1

Step-by-step explanation:

f ( x ) = x³ + 2 x² - 5 a x - 7

When divided by x + 1 :

remainder = f ( - 1 )

⇒ ( - 1 )³ + 2 ( -1 )² - 5 ( - 1 ) a - 7

⇒ - 1 + 2 + 5 a - 7

⇒ 5 a - 6

R1 = 5 a - 6

When g ( x ) is divided by x + 2 , remainder is - 2

f ( - 2 ) = 2 ( -2 )³ + a ( - 2 )² - 6 ( - 2 ) + 2

⇒ - 16 + 4 a + 12 + 2

⇒ 4 a - 2

2 R1 +  R2 = 0

⇒ 2 ( 5 a - 6 ) + 4 a - 2 = 0

⇒ 10 a - 12 + 4 a - 2 = 0

⇒ 14 a - 14 = 0

⇒ 14 a = 14

⇒ a = 14/14

⇒ a = 1

The value of a is 1 .