NAME – Janendra PinguaCLASS- IX - A

A presentation on

WHAT IS A POLYNOMIAL

On the basis of degree

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

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 = -3Hence zeroes of f(x) are α = -4 and β = -3.

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