To find a quadratic polynomial given its zeros, you can use the fact that if a polynomial has zeros at r and s, it can be expressed in the factorized form:
f(x) = (x - r)(x - s)
In this case, the zeros are 4 and 2. Plugging these values into the formula gives:
f(x) = (x - 4)(x - 2)
Now, we can expand this equation:
f(x) = x^2 - 2x - 4x + 8
Combining like terms, we get:
f(x) = x^2 - 6x + 8
Thus, the quadratic polynomial whose zeros are 4 and 2 is:
f(x) = x² – 6x + 8
This polynomial can now be used in various mathematical applications, such as graphing or solving equations involving these zeros.