Question

The polynomial x^3+ 2x^2 – 5ax –8 and x^3+ ax^2– 12x –6 when divided by (x–2) and (x–3) leave remainder p and q respectively. If q – p=10 Find the value of a.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Ans_ a=33/19

Given x^3+2x^2-5ax-8 and x^3+ax^2-12x-6 when divided by x-2 and x-3 respectively then remainders are p and q

q-p=10

a=?

Let f(x)=x^3+2x^2-5ax-8

p (x)=x^3+ax^2-12x-6

By remainder theorem

f (2)=2^3+2×2^2-5a (2)-8

p=8+8-10a-8

p=8-10a

p (3)=3^3+a×3^2-12 (3)-6

q=27+9a-36-6

q=27-42+9a

q=-15+9a

Given q-p=10

-15+9a-8+10a=10

-23+19a=10

19a=10+23

19a=33

a=33/19