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Find a quadratic equation whose roots are , such that +=3 and

Question

Find a quadratic equation whose roots are $α, β$ such that $α + β = 3$ and $α^{3} + β^{3} = 9$ .

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Find a quadratic equation whose roots are

α, β

such that

α + β = 3

and

α^{3} + β^{3} = 9

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Given

α + β = 3 - - - (1)

α^{3} + β^{3} = 9 - - - - (2)

From

(2)

we get,

(α + β)^{3} - 3 α β (α + β) = 9

or,

27 - 9 α β = 9

[using

(1)

]

or,

9 α β = 18

or,

α β = 2 - - - (3)

Now, the quadratic equation whose roots are

α

β

x^{2} - (α + β) x + α β = 0

or,

x^{2} - 3 x + 2 = 0

. [ using

(1)

(3)

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Question Text	Find a quadratic equation whose roots are $α, β$ such that $α + β = 3$ and $α^{3} + β^{3} = 9$ .
Answer Type	Text solution:1
Upvotes	150