Answer:
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.
The roots of a quadratic equation are the values of x that make the equation equal to zero.
Given that the roots of the quadratic equation are (3+√5) and (3-√5), we can set the quadratic equation equal to zero and substitute the roots for x:
ax^2 + bx + c = 0
(x - (3+√5))(x - (3-√5)) = 0
(x - 3 - √5)(x - 3 + √5) = 0
(x - 3 - √5)(x - 3 + √5) = (x-3)^2 - (√5)^2 = (x-3)^2 - 5 = 0
x^2 - 6x + 9 - 5 = 0
x^2 - 6x + 4 = 0
So the quadratic equation whose roots are (3+√5) and (3-√5) is x^2 - 6x + 4 = 0
Explanation: