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10th Board Practice (Section B)

Problem

The zeros of a polynomial p(x) are α, β, and γ.
p(x)=2x3+bx2+cx15
αβ+βγ+γα=10 and α+β+γ=17.
Find the value of c.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi