1-6 Finding an unknown coefficient from a condition on the roots
Point 6 of 11 — Unit 1: Complex Numbers, the Quadratic Equation, Sign of a Function and Quadratic InequalitiesQuestion bank: 0 questions (0 with pictures)
06 1-6 Finding an unknown coefficient from a condition on the roots
Two equal roots → putΔ = 0 and solve for the unknown.
Two different real roots →Δ > 0; no real roots →Δ < 0; two real roots (allowing equality) → Δ ≥ 0.
Toprove that the roots are real for every value of the parameter, compute Δ and rewrite it as a square plus a positive term, e.g. Δ = (k − 3)² + 4 ≥ 0 for all k — so the equation is never without real roots.
If one root r is given, substitute it: ar² + br + c = 0 gives the unknown coefficient directly.
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