To find a quadratic polynomial given its zeros, we can use the fact that if a polynomial has zeros at p and q, it can be expressed in the form:
f(x) = k(x – p)(x – q)
Here, p = 4 and q = 2. We can substitute these values into the equation.
Using k = 1 for simplicity, we have:
f(x) = (x – 4)(x – 2)
Next, we’ll expand the expression:
f(x) = x^2 – 2x – 4x + 8
This simplifies to:
f(x) = x^2 – 6x + 8
Thus, the quadratic polynomial whose zeros are 4 and 2 is:
f(x) = x^2 – 6x + 8