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samson27:
yes the question is
if α+β =5 and αcube + βcube =35 find the quadratic equation whose roots are α and β
this is the correct question bro
ok! let me edit the answer!
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Given : α + β = 5 ----- (1)
Given : α^3 + β^3 = 35 ---- (2)
On Cubing Equation (1) on both sides, we get
⇒ (α + β)^3 = (5)^3
⇒ α^3 + β^3 + 3αβ(α + β) = 125
⇒ 35 + 3αβ(5) = 125 {from (2)}
⇒ 3αβ(5) = 125 - 35
⇒ 3αβ(5) = 90
⇒ 3αβ = 90/5
⇒ 3αβ = 18
⇒ αβ = 18/3
⇒ αβ = 6.
We know that when α and β are roots of quadratic equation, then equation can be:
⇒ x^2 - (α + β)x + αβ = 0.
Therefore the required quadratic equation is:
⇒ x^2 - (5)x + (6) = 0
⇒ x^2 - 5x + 6 = 0.
Hope it helps!
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