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The sum of two roots of a quadratic equation is 5 and sum thei

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The sum of two roots of a quadratic equation is $5$ and sum their cubes is $35$ the equation. Find the equation.

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The sum of two roots of a quadratic equation is

5

and sum their cubes is

35

the equation. Find the equation.

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Let the two roots be

α

and

β

α + β = 5

α^{3} + β^{3} = 35

(α + β)^{3} = α^{3} + β^{3} + 3 α β (α + β)

(5)^{3} = 35 + 3 α β (5)

125 = 35 + 15 α β

90 = 15 α β

∴ \frac{90}{15} = α β

∴ α β = 6

Quadratic

E q^{n}

x^{2} - (s u m o f roo t s) x + p ro d u c t o f roo t s = 0

x^{2} - (α + β) x + α β = 0

x^{2} - 5 x + 6 = 0

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Question Text	The sum of two roots of a quadratic equation is $5$ and sum their cubes is $35$ the equation. Find the equation.
Answer Type	Text solution:1
Upvotes	150