Multiple choice

(\text{sin}\alpha \text{ and } \text{cos}\alpha \text{ are the roots of the equation } x^2 - abx + c = 0 \text{ then})

  1. $\(a^2c^2 - 2b - 1 = 0\)$
  2. $\(a^2 - ac + b^2 = 0\)$
  3. $\(a^2b^2 - 2c - 1 = 0\)$
  4. $\(a^2 - ab + ac = 0\)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given sin α and cos α are roots of x² - abx + c = 0. By Vieta's formulas: sum of roots = sin α + cos α = ab, product = sin α × cos α = c. We know sin²α + cos²α = 1. Using (sin α + cos α)² = sin²α + cos²α + 2sin α cos α, we get (ab)² = 1 + 2c, which simplifies to a²b² - 2c - 1 = 0. Option C is correct.

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