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If x4 – kx3 + 10×2 + 1x – 3 is divisible by (x -…

If x4 – kx3 + 10x2 + 1x – 3 is divisible by (x – 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and 1
  • A.
    k = -7, 1 = -15
  • B.
    k = -15, 1 = -7
  • C.
    k = (frac{15}{3}) , 1 = -7
  • D.
    k = (frac{7}{3}) , 1 = -17
Correct Answer: Option A
Explanation

If k = -7 is put as -15, the equation x4 – kx3 + 10x2 + 1x – 3 becomes x4 – (7x3) + 10x2 + (15)-3 = x4 + 7x3 + 10x2 – 15x – 3
This equation is divisible by (x – 1) and (x + 2) with the remainder as 27
k = -7, 1 = -15