This document summarizes key properties of polynomials, including that the sum of zeros is equal to the negative of the coefficient of x^2, and the product of zeros is equal to the negative of the constant term. It provides an example of finding the zeros of the polynomial x^2 + 7x + 12 and verifying these properties. It also gives an example of constructing a quadratic polynomial with given zeros of 4 and 1.

1. A presentation on
NAME - Partik
CLASS- X - C

2. WHAT IS A
POLYNOMIAL

4. On the basis of degree

7.  Let α, β and γ be the zeroes of the polynomial ax³ + bx² + cx + d
 Then, sum of zeroes(α+β+γ) = -b = -(coefficient of x²)
a coefficient of x³
αβ + βγ + αγ = c = coefficient of x
a coefficient of x³
Product of zeroes (αβγ) = -d = -(constant term)
a coefficient of x³

8. I) Find the zeroes of the polynomial x² + 7x + 12and verify the relation between
the zeroes and its coefficients.
f(x) = x² + 7x + 12
= x² + 4x + 3x + 12
=x(x +4) + 3(x + 4)
=(x + 4)(x + 3)
Therefore,zeroes of f(x) =x + 4 = 0, x +3 = 0 [ f(x) = 0]
x = -4, x = -3
Hence zeroes of f(x) are α = -4 and β = -3.

10. 2) Find a quadratic polynomial whose
zeroes are 4, 1.
sum of zeroes,α + β = 4 +1 = 5 = -b/a
product of zeroes, αβ = 4 x 1 = 4 = c/a
therefore, a = 1, b = -4, c =1
as, polynomial = ax² + bx +c
= 1(x)² + { -4(x)} + 1
= x² - 4x + 1
The end