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Question
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
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Solution
Let a, β be the roots of the required quadratic equation:
Then, a = `sqrt(3) and beta = 3sqrt(3)`
a + β = `sqrt(3) + 3sqrt(3) and abeta = sqrt(3) xx 3sqrt(3)`
∴ a + β = `4sqrt(3) and abeta = 9`
Required quadratic equation
x2 - (a + β)x + aβ = 0
⇒ x2 - 4`sqrt(3)x + 9 = 0`.
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