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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 â€“ 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 $\frac{\text{- Constant term}}{\text{Coefficient of}{\text{x}}^{\text{}}}$ .

General form of quadratic polynomial is ax^{2} + bx +c where a â‰ 0. There are two zeroes of quadratic polynomial.

Sum of zeroes = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- Coefficient of x}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$

Product of zeroes =$\frac{\text{c}}{\text{a}}$ = $\frac{\text{Constant term}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$ .

General form of cubic polynomial of ax^{3} + bx ^{2}+ cx + d where a â‰ 0. There are three zeroes of cubic polynomial.

The sum of zeroes of the cubic polynomial = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- coefficient of}{\text{x}}^{\text{2}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Sum of the product of zeroes taken two at a time = $\frac{\text{c}}{\text{a}}$ = $\frac{\text{coefficient of}{\text{x}}^{}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Product of zeroes = $\frac{\text{-d}}{\text{a}}$ = $\frac{\text{- Constant term}{\text{}}^{\text{}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$ .

A real number k is a zero of a polynomial of p(x) if p(k) = 0.

If a is zero of a polynomial p(x) then (x â€“ a) is a factor of p(x).

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 $\frac{\text{- Constant term}}{\text{Coefficient of}{\text{x}}^{\text{}}}$ .

General form of quadratic polynomial is ax

Sum of zeroes = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- Coefficient of x}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$

Product of zeroes =$\frac{\text{c}}{\text{a}}$ = $\frac{\text{Constant term}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$ .

General form of cubic polynomial of ax

The sum of zeroes of the cubic polynomial = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- coefficient of}{\text{x}}^{\text{2}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Sum of the product of zeroes taken two at a time = $\frac{\text{c}}{\text{a}}$ = $\frac{\text{coefficient of}{\text{x}}^{}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Product of zeroes = $\frac{\text{-d}}{\text{a}}$ = $\frac{\text{- Constant term}{\text{}}^{\text{}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$ .

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 â€“ 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 $\frac{\text{- Constant term}}{\text{Coefficient of}{\text{x}}^{\text{}}}$ .

General form of quadratic polynomial is ax^{2} + bx +c where a â‰ 0. There are two zeroes of quadratic polynomial.

Sum of zeroes = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- Coefficient of x}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$

Product of zeroes =$\frac{\text{c}}{\text{a}}$ = $\frac{\text{Constant term}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$ .

General form of cubic polynomial of ax^{3} + bx ^{2}+ cx + d where a â‰ 0. There are three zeroes of cubic polynomial.

The sum of zeroes of the cubic polynomial = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- coefficient of}{\text{x}}^{\text{2}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Sum of the product of zeroes taken two at a time = $\frac{\text{c}}{\text{a}}$ = $\frac{\text{coefficient of}{\text{x}}^{}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Product of zeroes = $\frac{\text{-d}}{\text{a}}$ = $\frac{\text{- Constant term}{\text{}}^{\text{}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$ .

A real number k is a zero of a polynomial of p(x) if p(k) = 0.

If a is zero of a polynomial p(x) then (x â€“ a) is a factor of p(x).

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 $\frac{\text{- Constant term}}{\text{Coefficient of}{\text{x}}^{\text{}}}$ .

General form of quadratic polynomial is ax

Sum of zeroes = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- Coefficient of x}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$

Product of zeroes =$\frac{\text{c}}{\text{a}}$ = $\frac{\text{Constant term}}{\text{Coefficient of}{\text{x}}^{\text{2}}}$ .

General form of cubic polynomial of ax

The sum of zeroes of the cubic polynomial = $\frac{\text{-b}}{\text{a}}$ = $\frac{\text{- coefficient of}{\text{x}}^{\text{2}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Sum of the product of zeroes taken two at a time = $\frac{\text{c}}{\text{a}}$ = $\frac{\text{coefficient of}{\text{x}}^{}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$

Product of zeroes = $\frac{\text{-d}}{\text{a}}$ = $\frac{\text{- Constant term}{\text{}}^{\text{}}}{\text{Coefficient of}{\text{x}}^{\text{3}}}$ .