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Question
Two roots of quadratic equation is given ; frame the equation.
\[1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}\]
Solution
\[1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}\]
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 \[x^2 - 2x - 44 = 0\]
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Activity:
Let α = 2 and β = 5 are the roots of the quadratic equation.
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