To find the quadratic equation with roots \(3+i\) and \(3-i\), we can use Vieta's formulas. The sum of the roots is given by:
\[ (3+i) + (3-i) = 3 + i + 3 - i = 6 \]
The product of the roots is:
\[ (3+i)(3-i) = 3^2 - (i^2) = 9 - (-1) = 9 + 1 = 10 \]
Using the general form of a quadratic equation \(x^2 - (sum\ of\ roots)x + (product\ of\ roots) = 0\), we can substitute the values we found:
\[ x^2 - 6x + 10 = 0 \]
Thus, the quadratic equation that has the roots \(3+i\) and \(3-i\) is:
\[ x^2 - 6x + 10 = 0 \]
So, the correct response is: \(x^2 - 6x + 10 = 0\)
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