Notes On Relationship between Zeroes and Coefficients of a Polynomial - CBSE Class 10 Maths
A polynomial is an algebraic expression consisting of multiple terms. There are various types of polynomials such as linear, quadratic, cubic and so on. A real number k is a zero of a polynomial of p(x) if p(k) = 0. Factor Theorem: If a is zero of a polynomial p(x) then (x – a) is a factor of p(x). Relationship betweeen Zeroes and coefficients of a Polynomial The general form of linear polynomial is p(x) = ax+b, its zero is $\frac{\text{-b}}{\text{a}}$ .i.e.x = $\frac{\text{-b}}{\text{a}}$ or   . General form of quadratic polynomial is ax2 + bx +c where a ≠ 0. There are two zeroes of quadratic polynomial. Sum of zeroes = $\frac{\text{-b}}{\text{a}}$ =   Product of zeroes = =   . General form of cubic polynomial of ax3 + bx 2+ cx + d where a ≠ 0. There are three zeroes of cubic polynomial. The sum of zeroes of the cubic polynomial = $\frac{\text{-b}}{\text{a}}$ =   Sum of the product of zeroes taken two at a time = $\frac{\text{c}}{\text{a}}$ =      Product of zeroes = $\frac{\text{-d}}{\text{a}}$ =   .

#### Summary

A polynomial is an algebraic expression consisting of multiple terms. There are various types of polynomials such as linear, quadratic, cubic and so on. A real number k is a zero of a polynomial of p(x) if p(k) = 0. Factor Theorem: If a is zero of a polynomial p(x) then (x – a) is a factor of p(x). Relationship betweeen Zeroes and coefficients of a Polynomial The general form of linear polynomial is p(x) = ax+b, its zero is $\frac{\text{-b}}{\text{a}}$ .i.e.x = $\frac{\text{-b}}{\text{a}}$ or   . General form of quadratic polynomial is ax2 + bx +c where a ≠ 0. There are two zeroes of quadratic polynomial. Sum of zeroes = $\frac{\text{-b}}{\text{a}}$ =   Product of zeroes = =   . General form of cubic polynomial of ax3 + bx 2+ cx + d where a ≠ 0. There are three zeroes of cubic polynomial. The sum of zeroes of the cubic polynomial = $\frac{\text{-b}}{\text{a}}$ =   Sum of the product of zeroes taken two at a time = $\frac{\text{c}}{\text{a}}$ =      Product of zeroes = $\frac{\text{-d}}{\text{a}}$ =   .

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