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Question

Form the quadratic equation whose roots are
3 and 10

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Solution

Let α = 3 and β = 10
Then, α+β = 3 + 10 = 13 and αβ=3×10 = 30
We know that if α and β are the roots of a quadratic equation, the equation is
x2 – (α+β)x + αβ = 0
On substituting α+β = 13 and αβ=30 , we get:
x2 – 13x + 30 = 0

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