Question

1. If a polynomial of (X) = Ax³+bx-c is divisible by the polynomial g(X) = X² + bx +c then ad=?
(A) 1 (B) 1/c-1 (C) -1/c (D) 1/c

2. In an AP it is given that tp+1=2tq+1 Find a:d
(A) 2tp+q+1 (B) 2t p+q+1 (C) p-q/1 (D) q-p /1

Answer 1

1.  f(x) = a x^3 +b x - c is divisible by g(x)= x^2 + b x + c 
           = ( x^2 + b  x + c) ( a x - 1),
          we can write (ax - 1) from the coefficients of  x^3 and constant term in f(x).
      expanding expressions and comparing, ab = 1 ,  c = 1/a^2   ac = b

2.  A.P. = a, a+d, a+2d,....
        t_(p+1)  = 2 * t_(q+1) 
        a + p d = 2 a + 2 q d  
             a = (p - 2q) d