Ch 2 explores the relationship between zeroes of a polynomial and its coefficients. Students learn to verify these relationships for quadratic and cubic polynomials, and apply the division algorithm.
For p(x) = ax² + bx + c with zeroes α and β: sum of zeroes α + β = −b/a, product of zeroes αβ = c/a. A quadratic has at most 2 zeroes. Graphically, zeroes are x-intercepts of the parabola.
For p(x) = ax³ + bx² + cx + d with zeroes α, β, γ: α+β+γ = −b/a, αβ+βγ+γα = c/a, αβγ = −d/a. A cubic polynomial has at most 3 zeroes.
For polynomials p(x) and g(x) with degree g ≤ degree p: p(x) = g(x)·q(x) + r(x), where r(x) = 0 or degree r < degree g. This is used to find remaining zeroes when some are known.
Download: https://ncert.nic.in/textbook/pdf/jemh102.pdf | Complete book: https://ncert.nic.in/textbook/pdf/jemh1ps.zip
A quadratic polynomial can have 0, 1, or 2 zeroes. When it has exactly one zero, the two zeroes are equal (repeated root), and the graph touches the x-axis at exactly one point.
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