Question

Two roots of quadratic equation is given ; frame the equation.

\[1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}\] 

Answer 1

\[1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}\]

Sum of roots = \[1 - 3\sqrt{5} + 1 + 3\sqrt{5} = 2\]

Product of roots = \[\left( 1 - 3\sqrt{5} \right)\left( 1 + 3\sqrt{5} \right) = 1 - 45 = - 44\]

The general form of the quadratic equation is \[x^2 - \left( \text{ Sum of roots } \right)x + \text{ product of roots } = 0\]

So, the quadratic equation will be  \[x^2 - 2x - 44 = 0\]