Polynomial For Class 10

We are already aware of the term Polynomial that we studied in class 9. Let us now learn more about polynomial.

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 (\(\alpha \beta = \frac{c}{a}\))

Polynomial For Class 10

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 \(r(x)< degree \;\; g(x)\)<

Polynomial For Class 10

Polynomial For Class 10

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