To find a quadratic polynomial with the given zeroes, we can use the fact that the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0 are related to the coefficients of the quadratic equation.
1. Given zeroes: 5-√3 and 5+√3
2. Sum of the zeroes: (5-√3) + (5+√3) = 10
3. Product of the zeroes: (5-√3)(5+√3) = 25 - 3 = 22
Now, the quadratic equation can be written in the form:
x^2 - (sum of the zeroes)x + product of the zeroes = 0
Substitute the sum and product values:
x^2 - 10x + 22 = 0
Therefore, the quadratic polynomial with zeroes 5-√3 and 5+√3 is:
x^2 - 10x + 22
