Mathematics Class 10
Polynomials
Find a polynomial's zeros, read them from split brackets, and use the coefficient relations.
13 lessons · ~85 min total
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Lessons in this topic
- 0 Start here A roadmap: the zero, the brackets that hand it over, the curve, and two coefficient relations. · 4 min You are here
- 1 The input that lands on zero A zero of a polynomial is an input where the value is 0, found by one substitution. · 6 min
- 2 Factors hand over their zeros A product is 0 when a factor is 0, so split brackets hand over their zeros for free. · 7 min
- 3 The curve and its crossings A quadratic draws a parabola, and it meets the x-axis exactly at the zeros, at most twice. · 7 min
- 4 The sum the zeros keep When a quadratic has zeros, they add up to −b/a. · 7 min
- 5 Where the two relations come from Opening (x − p)(x − q) proves the sum relation and names its twin: the product is c/a. · 7 min
- 6 Building it from its zeros Two zeros fix the quadratic x² − Sx + P, and any nonzero multiple works too. · 7 min
- 7 What the relations tell you first If a quadratic has zeros, the signs of P and S say where they sit. · 7 min
- 8 Finding values without the zeros Find α² + β² or 1/α + 1/β from S and P, with no zero found. · 7 min
- 9 The cubic keeps three relations A cubic with three zeros keeps three relations. They come from a, b, c and d. · 8 min
- 10 Checkpoint: relations, building and the cubic Five quick checks on sums, products, building backwards and the cubic. · 6 min
- 11 The big picture The whole chapter on one screen: a zero, split brackets, a curve, and the coefficient relations. · 4 min
- 12 Track quiz Cheat-sheet table plus a reveal quiz, one question per idea. · 8 min
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