Zeros of Polynomial : It is a solution to the polynomial equation, P(x) = 0. It is that value of x that makes the polynomial equal to 0.

The value of a polynomial f(x) at x = a is obtained by substituting x = a in the given polynomial and is denoted by f(a) which is Zeros of Polynomial.

Find the value of f(x) = x

f (x) = x

f(-1) = (-1)

= -1 -2 – 2 – 4

= - 9

ax

If α and β are the roots of the equation then

Sum of zeroes = α + β = Product of zeroes = αβ = |

From the above the equation of polynomial is given by

1) Write the equation of the polynomial, if sum of zeroes = -8 and product of zeroes is 15

Product of zeroes = αβ = 15

Equation is x

x

x

ax

Sum of zeroes = α + β+γ = - b/a Sum of the product of zeroes taken two at a time = αβ + βγ+αγ = c/a Product of zeroes = αβγ = -d/a |

The cubic polynomial can be written as

1) Find the cubic polynomial with the sum, sum of the product of zeroes taken two at a time, and product of its zeroes as 2,-7 ,-14 respectively.

If α,β and γ are the zeroes of a cubic polynomial then

x

α + β+γ = 2

αβ + βγ+αγ = -7

αβγ = -14

x

x

• Degree of the Polynomial

• Zeros of Polynomial

• Remainder Theorem

• Find remainder by Synthetic Division

• Rational root test in Polynomial

• Solved Examples on Polynomial

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