Question

Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between
zeroes and coefficients of the polynomial.

Answer 1

Answer:

The number of zeroes of a polynomial is equal to the degree of the polynomial, and there is a well-defined mathematical relationship between the zeroes and the coefficients.

Step-by-step explanation:

Polynomials can be linear (x), quadratic (x2), cubic (x3) and so on, depending on the highest power of the variable.

The number of zeroes of a polynomial is equal to the degree of the polynomial, and there is a well-defined mathematical relationship between the zeroes and the coefficients. Mathematically, 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).

Here, the real number k is said to be a zero of the polynomial of p(x), if p(k) = 0.

Simply put, the zeroes of a polynomial function are the solutions to the equation you get, when you set the polynomial equal to zero.

Let us understand the difference between zeros and roots in a polynomial equation.

A zero is a value for which a polynomial is equal to zero.

When you set a polynomial equal to zero, then you have a polynomial equation where the equations roots are same as the polynomial’s zeroes.

A root is a value for which a polynomial equation is true.

Example: The polynomial x-5 has one zero, that is x = 5. And the polynomial equation x-5 = 0 has one root, that is, x = 5.