Question

If r and s be the remainders when the polynomials ( x cube + 2x square _ 5ax _ 7) and (x cube +ax square _ 12ax +6) are divided by (x+1) and (x_2) respectively and 2r +s =6, find the value of a.

Answer 1

Let p(x) = x3 +2x2 -5ax -7 and q(x) = x3 +ax2 -12ax +6
By remainder theorem
p(-1) = r

or (-1)3 + 2(-1)2 – 5a(-1) – 7 = -1 + 2 +5a – 7 = 5a – 6 = r
Also,
q(2) = s
or 23 +a(2)2 -12a(2) +6 = 8 + 4a – 24a + 6 = 14 – 20a = s
Hence,
2r + s = 6
or 10a – 12 + 14 – 20a = 6
or 2 – 10a = 6
or a = –0.4

Hope it helps........

Answer 2

Plz see the photo for answer.

Mark as brainliest if you like it. Thanks!