<\b>Forming a Quadratic Polynomial with Given Zeroes:
• Let the quadratic polynomial be of the form: f(x) = ax^2 + bx + c
• Given one zero is 2 + √3 and the sum of zeroes is 4.
• Since the sum of zeroes is 4, the other zero can be found by subtracting the given zero from the sum, i.e., 4 - (2 + √3) = 2 - √3
<\b>Using the Zeroes to Form the Polynomial:
• The product of the zeroes is the constant term divided by the leading coefficient. So, (2 + √3)(2 - √3) = c/a
• Simplifying, we get 4 - 3 = c/a, which gives c = a
• The sum of the zeroes is also related to the coefficients of the polynomial. So, -(b/a) = 4
• Substituting the values of c and the sum of zeroes in the above equation, we get -(b/a) = 4
<\b>Solving for the Coefficients:
• We have the system of equations: c = a and -(b/a) = 4
• Substituting c = a in the second equation, we get -b/a = 4, which gives b = -4a
• Therefore, the quadratic polynomial can be written as f(x) = ax^2 - 4ax + a
<\b>Conclusion:
• The quadratic polynomial with one zero as 2 + √3 and the sum of zeroes as 4 is f(x) = ax^2 - 4ax + a, where a is a constant value.