Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.
8x2−x+16
Let, α & β be zeroes.
Given, α+β=18; αβ=2
Therefore required polynomial is p(x)=k[x2−(α+β)x+αβ] where k is a real number.
Now, consider p(x)=k[x2−18x+2]
p(x)=k[8x2−x+168]
p(x)=k×18[8x2−x+16]
Let's take k = 8
(Note: multiplying a polynomial with a non-zero constant doesn't change the zeroes of the polynomial).
⇒p(x)=8x2−x+16
Therefore, (8x2−x+16) is a polynomial with 18 as the sum and 2 as product of its zeroes.