Answer:
the quadratic equation with roots 5+√3 and 5-√3 is x^2 - 10x + 22 = 0.
Explanation:
If the roots of a quadratic equation are 5 +√3 and 5 -√3, then we know that the factors of the quadratic equation are (x - (5+√3))(x - (5-√3)) = 0.
To simplify this expression, we can use the difference of squares formula:
(x - (5+√3))(x - (5-√3)) = [(x - 5) - √3][(x - 5) + √3] = (x - 5)^2 - 3
Therefore, the quadratic equation with roots 5+√3 and 5-√3 is:
(x - 5 + √3)(x - 5 - √3) = 0
Expanding the left-hand side and simplifying, we get:
x^2 - 10x + 22 = 0
Therefore, the quadratic equation with roots 5+√3 and 5-√3 is x^2 - 10x + 22 = 0.