Final answer:
A polynomial equation with integer coefficients having roots y = 9 and y = -9 is y² - 81 = 0, obtained by multiplying the factors (y - 9) and (y + 9).
Step-by-step explanation:
To write a polynomial equation with integer coefficients that has the given roots y = 9 and y = -9, we start with the fact that if a number a is a root of a polynomial, then (x - a) is a factor of that polynomial. In our case, the roots given are 9 and -9. Therefore, the factors associated with these roots are (y - 9) and (y + 9).
To find the polynomial, we multiply the factors together which will give us the equation:
(y - 9)(y + 9) = y² - 81
Thus, the polynomial equation with integer coefficients that has roots y = 9 and y = -9 is y² - 81 = 0.