Question

Form a quadratic equation with rational coefficients, one of whose roots is $3+\sqrt{5}$.

Answer 1

If $3+\sqrt{5}$ is one root, then the other root is $3-\sqrt{5}$.

Sum of the roots = 6

Product of the roots = 4
If $p,q$ are roots of a quadratic equation, then the equation is $x^2-(p+q)x+pq=0$

Thus, the required equation is $x^2-6x+4=0$

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