To determine which polynomial has zeros at x = 4 and x = 7, we need to recognize that if a polynomial has a zero (or root) at a particular value, this can be expressed in factored form. In this case, since the polynomial has zeros at these two values, we can express it as:
(x – 4)(x – 7)
When the polynomial is formed using these roots, it indicates that substituting x = 4 or x = 7 into the polynomial will yield a result of zero:
To find a specific polynomial, we can expand this expression:
(x – 4)(x – 7) = x^2 – 7x – 4x + 28 = x^2 – 11x + 28
Thus, a polynomial that has zeros at x = 4 and x = 7 is:
x^2 – 11x + 28
This polynomial will yield 0 for both x = 4 and x = 7, confirming that it indeed has the specified zeros.