The sum of zeroes of a quadratic polynomial is 3 4 and product is 1 4 find the polynomial equation

Given,

Sum of zeroes = α+β = 4

Product of zeroes = αβ = 1

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-

x2–[α+β]x+αβ = 0

x2–4x+1 = 0

Thus, x2–4x+1 is the quadratic polynomial.