The Number of the polynomials having zeroes as -2 and 5 is
a)1
b) 2
c) 3
d) more than 3
Correct option: (d) more than 3
Polynomials
An algebraic expression in which the exponents of all variables are a whole number is called a polynomial. The power of variables of any polynomial should be a non-negative integer. We cannot perform division operations by a variable in any polynomial, but a polynomial contains constants and variables.
Terms of Polynomials
A part of an expression that is separated by the operators + or – is defined as polynomial terms.
For example- The polynomial expression
5𝑥³−4𝑥²+8𝑥−12 has four terms of polynomial expressions.
Degree of Polynomials
The degree of the polynomial is defined as the highest or greatest power of a variable in a polynomial. This is used to determine the maximum number of solutions of a polynomial equation. The sum of the power of the variables is equal to the degree of a polynomial with more than one variable in it.
Correct option: (d) more than 3
Explanation-
Let us assume the zeroes of the polynomial as a= -2 and b = 5.
The general form of a polynomial with a and b as the zeroes is:
k [x² – (a + b) x + a*b], k is any real number
= k [x² – (-2 + 5) x + (-2) (5)]
= k (x² -3x – 10)
Therefore, more than three polynomial expressions can have the zeroes as -2 and 5.