Question

. The polynomials ax3 – 3x2 +4 and 2x3 – 5x +a when divided by (x – 2) leave the remainders p and q respectively. If p – 2q = 4, find the value of a.

Sol.​

Answer 1

Answer:

a = 4

Step-by-step explanation:

See the SOLUTION carefully

Let f(x) = ax^3 - 3x^2 +4

g(x) = 2x^3 - 5x + a

Zero of ( x- 2 ) = 2

So,

f(2) = a(2)^3 - 3(2)^2 +4

= 8a -12 +4 = 8a - 8

p = 8a - 8 ..... (i)

g(2) = 2(2)^3 - 5(2) + a

= 16 - 10 + a = 6 + a

q = 6 + a ........ (ii)

Now,

p- 2q = 4

=> (8a - 8) - 2( 6+ a) =4

=> 8a -8 -12 - 2a = 4

=> 6a - 20 =4

=> 6a = 4 + 20 =24

=> a = 24 / 6 = 4

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