find the value of m and n so that the polynomial a^3 - ma^2 -13a + n has [a-1] and - Maths - Polynomials

Question

find the value of m and n so that the polynomial a^3 - ma^2
-13a + n has [a-1] and [a+3] as the factors

Abhishek Jha · Accepted Answer

Dear Student,
Here is the solution of your asked query:
The given polynomial is p(a)=a3-ma2-13a+nSince, a-1 is the factor of p(a), so we have;p(1)=0⇒13-m×12-13×1+n=0⇒1-m-13+n=0⇒n-m=12   
(i)also, a+3 is the factor of p(a), so we have;p(-3)=0⇒-33-m×-32-13×-3+n=0⇒-27-9m+39+n=0⇒9m-n=12   
(ii)From (i) and (ii) we get;n-m+9m-n=24⇒8m=24⇒m=3Then, n=12+3=15Therefore, m=3 and n=15
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find the value of m and n so that the polynomial a^3 - ma^2 -13a + n has [a-1] and [a+3] as the factors