Ch 4Theory of Equations — Class 12 Mathematics, concept-first.

By this point you have solved linear equations, and quadratic equations and inequations, in real depth — including, from the previous chapter, the exact relationship between a quadratic's two roots an…

A polynomial equation of degree has the form , with . Up to now you have solved linear and quadratic equations directly, but most equations that show up in real applications — in engineering, economic…

Write the general monic degree- equation as and let be its roots. Comparing this with the factored form and expanding, the coefficient of each power of turns out to be (up to a sign) one of the elemen…

A symmetric function of the roots is any expression built from that is unchanged if you permute the roots among themselves — for instance , , or for a cubic.

Dividing a polynomial by using the Remainder Theorem's coefficient pattern is called synthetic division — a compact bookkeeping scheme that avoids writing out the full long division.

A root of is said to have multiplicity if divides exactly but does not — equivalently, appears times among the roots counted in the Fundamental Theorem of Algebra.

Two useful “pairing” facts restrict what the roots of an equation can look like, depending on what kind of coefficients the equation has.

Sometimes the most efficient way to solve or analyse an equation is not to attack it directly, but to transform it into a related equation whose roots are a known function of the original roots (shift…

A polynomial is called reciprocal, and the equation a reciprocal equation, if its coefficient sequence read forwards is the same as read backwards, either exactly or up to an overall sign flip.

Sample papers and previous-year board questions for this subject.