Answer : Given data is, x2 – 3x + p = 0 → (1) a and b are roots of (1) So, (x + a)(x + b) = 0 x2 - (a + b)x + ab = 0 So, a + b = 3 and ab = p → (2) Given data is, x2 – 12x + q = 0 → (3) c and d are...
Answer : Cross multiplying (1) and expanding, (a + bx)(b – cx) = (b + cx)(a-bx) ab – acx + b2x – bcx2 = ba –b2x + acx – bcx2 2b2x = 2acx b2 = ac → (i) If three terms are in GP, then the middle term...
Answer : We need to prove that the product of the terms equidistant from the beginning and end is the product of first and last terms in a finite GP. Let us first consider a finite GP. A, AR,...
Answer : As per the question, a, b and c are the pth, qth and rth term of GP. Let us assume the required GP as A, AR, AR2, AR3… Now, the nth term in the GP, an = ARn-1 pth term, ap = ARp-1 = a → (1)...