Polynomial For Class 10

In a polynomial, the highest power of the polynomial is referred as the degree of the polynomial. A polynomial with degree 1 is known as linear polynomial, polynomial with degree 2 is binomial or quadratic polynomial, whereas with degree three is cubic polynomial.

For any given polynomial, the value of x obtained by substituting the value of polynomial as 0 is known as the zero of the polynomial. These are also termed as roots of the equation.The Graphical meaning of the zeros of the polynomial is that, the curve cuts the x axis a point (k,0), where k is the root of the polynomial.

Note- A polynomial of degree n will have n roots.

A quadratic equation $ax^{2}+bx+c=0$ will have 2 roots, say $\alpha$ and \beta\).

The sum of roots($\alpha + \beta = -\frac{b}{a}$)

Product of the roots ($\alpha \beta = \frac{c}{a}$)

Division algorithm of Polynomial-

The division algorithm states that any given polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that,

$p(x) = g(x)\times q(x)+ r(x)$

where, $r(x)=0$ and degree $r(x)< degree \;\; g(x)$<

Practise This Question

If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3+b3+c3 is equal to