3. WHAT IS A POLYNOMIAL?
A polynomial is an expression made with constants,
variables and exponents, which are combined using
addition, subtraction and multiplying but not division.
The exponents can only be o,1,2,3,4….. etc.
A polynomial cannot have infinite no. of terms.
10. VALUE OF A POLYNOMIAL
If ƒ(x) is a polynomial and α is any
real number, then the real number
obtained by replacing x by α in ƒ(x), is
called value of a polynomial.
11. ZEROES OF A POLYNOMIAL
A real number α is a zero of a polynomial
ƒ(x) if ƒ(α)=0.
12. RELATIONSHIP BETWEEN THE ZEROES
AND COEFFICIENTS OF A QUADRATIC
Let α and β be the zeroes of the polynomial ax²+bx+c=0.
Sum of zeroes (α+β)= -b/a
= -(coefficient of x)/ coefficient of x²
Product of zeroes (αβ)= c/a
= constant term/ coefficient of x²
13. RELATIONSHIP BETWEEN THE ZEROES
AND COEFFICIENTS OF A CUBIC
Let α, β and γ are the zeroes of the polynomial ax³+bx²+cx+d=0.
Sum of zeroes (α+β+γ)= -b/a
= -(coefficient of x²)/ coefficient of x³
= coefficient of x/ coefficient of x³
Product of zeroes (αβγ)= -d/a
= -(constant term)/ coefficient of x³