Which of the following polynomials has zeros at x = -4 and x = 7?
4x² - 7x - 11, 4x² - 49, 7x² - 4x + 28, x² - 3x - 28

Solution:

Given,

x = -4 and x = 7.

All the values of 'x' that make the polynomial equal to zero are called zeroes of a polynomial.

For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial.

The degree of the polynomial is the highest power of the variable x.

As we know that a standard polynomial of two degrees can be written as:

x² - (sum of zeroes) x + (product of zeroes)

Sum of zeroes = 3.

Product of zeroes = - 28.

we can write the polynomial using two given zeros as:

x² - 3x - 28.

Therefore, the polynomial is x² - 3x - 28.

Which of the following polynomials has zeros at x = -4 and x = 7?

Summary:

The polynomial x² - 3x - 28 has zeros at x = -4 and x = 7.