A polynomial is an expression consists of constants, variables and exponents.
If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).A real number k is said to be a zero of a polynomial p(x), if p(k) = 0
Geometrical meaning of the Zeroes of a Polynomial
Zeroes of the polynomials are the x coordinates of the point where the graph of that polynomial intersects the x-axis.
Relation between coefficient and zero's of the Polynomial:
(i) If α, β are zeroes / roots of p(x) = ax2 + bx + c, then
(ii) If α, β and γ are zeroes / roots of p(x) = ax3 + bx2 + cx + d
NCERT Solutions Ch 2 Polynomials