Engineering Board Exam Reviewer · Polynomials: Remainder and Factor Theorems · hard

The roots of x3-6x2+kx-6=0 are in arithmetic progression. Find k.

  1. 12
  2. 11
  3. 6
  4. 13

Answer

B. 11

Solution

Let the roots be a-d, a, a+d. The sum 3a=6 gives a=2. The product a(a2-d2)=6 2(4-d2)=6 d2=1. Then k is the sum of products in pairs: 3a2-d2=12-1=11. (The roots are 1,2,3.)

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