Question

The polinomials ax^3 + 3x^2 and 2x^3-5x+a when divided by x - 4 leaves reaminders A and B. Find a if 2A-B =0

Answer 1

a=4/43 when we substitute the value of A and B

Answer 2

Answer:

using reminder theorem

we will find f(x) of both polynomials at x-4=0 i.e x=4

first polynomial: f(x)=ax^3 + 3x^2

therefore,f(4)= a(4)^3 + 3(4)^2

                     =64a +48------>(given that it gives reminder A)

second polynomial:f(x)=2x^3-5x+a

therefore,f(4)=2(4)^3 - 5(4) + a

                    =128 - 20 + a

                    =108 + a ------->B(given that it gives reminder B)

also given,2A-B =0

therefore, 2A=B

i.e, 2[64a +48] = 108 + a  

     128a + 96 = 108 + a

     128a- a + 108 - 96

     127a = 12

      a = 12/127

Step-by-step explanation: