Algebra, Relations and Functions — The Relation Between the Two Roots of the Second Degree Equation and the Coefficients of its Terms

About this lesson

This unit focuses on the relationship between the roots of a quadratic equation (ax² + bx + c = 0) and its coefficients. It teaches how to find the sum and product of the roots without solving the equation, using the formulas L+M = -b/a and LM = c/a. The unit also covers forming a quadratic equation when its two roots are known, using the formula x² - (L+M)x + LM = 0. Additionally, it includes problems where one root is given (including complex roots) to find the other root and unknown coefficients, and exercises on forming new quadratic equations from the roots of a given equation (e.g., roots that are squares, doubled, or shifted). By the end, students should be able to apply these relationships to solve problems, determine unknown coefficients, and construct quadratic equations under various conditions.