Chapter 6 Quadratic EquationsPage | 1 QUADRATIC EQUATIONS Highlights:Solutions of quadratic equations, relations between its roots and coefficients problems leading to quadratic equations. Definitions & Review of ConceptsQuadratic Equation:Let f(x) be a quadratic polynomial, Then the equation f(x) = 0 is called a quadratic equation. The value of x satisfying f(x) = 0 are called its roots or zeros. Facts about Quadratic Equation: I: General information i) The general form of a quadratic equation is: ax2+ bx + c = 0 , where a, b, c ∈R and a ≠0. ii) If ?,?are the roots of ax2+ bx + c =0, then ?= −?+ ?2−4??2?and = −?−?2−4??2?iii) A quadratic equation has exactly two roots, may be real or imaginary or coincident. iv) If p + ?is a root of a quadratic equation, then its other root is p - ?.v) In ax2+ bx + c = 0, the expression D = b2–4 ac is called its discriminant. II Nature of roots of ax2+ bx + c = 0 : Let D = b2–4 ac be the discriminant of the given equations. Then, the roots of ax2+ bx + c = 0 are: i) Real and equal if D = 0; ii) Real, unequal and rational, when D > 0 and D is a perfect square; iii) Real, unequal and irrational, when D > 0 but D is not a perfect square; iv) Imaginary, if D < 0. v) Integers, when a = 1, b & c are integers and the roots are rational. III Condition that ax2+ bx + c is factorable into two linear factors: ax2+ bx + c is factorable into two linear factors only when b2–4 ac ≥0 IV: Relation between roots & coefficients: Let ?, ?