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If α is a root of , then the value of 5α² − 3α + 4 is:

Competition practiceAlgebra
  • A11
  • B7
  • C4
  • D−3

Step-by-Step Solution

A root satisfies its own equation, so 5α² − 3α − 7 = 0, which means 5α² − 3α = 7. Therefore 5α² − 3α + 4 = 7 + 4 = 11 — the messy root never has to be found. (7 stops at the value of 5α² − 3α; 4 assumes that quantity is zero; −3 simply quotes a coefficient.) Checking with the actual root α = (3 + √149)/10 ≈ 1.5207: 5(2.3125) − 3(1.5207) ≈ 11.563 − 4.562 = 7, and 7 + 4 = 11.
Answer: A) 11

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