Question

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

sum of their cubes is 35, find the equation​

Answer 1

Answer:

Let α and β be the roots of the quadratic equation.

According to the given conditions,  

α + β = 5 and α3 + β3 = 35  

Now, (α + β)3 = α3 + 3α2β + 3αβ2 + β3

∴ (α + β)3 = α3 + β3 + 3αβ (α + β)  

∴ (5)3 = 35 + 3αβ(5)

∴ 125 = 35 + 15αβ  

∴ 125 – 35 = 15αβ

∴ 15αβ = 90  

αβ = 90/15

∴ αβ = 6  

∴ The required quadratic equation is  x2 – (α + β)x + αβ = 0  

∴ x2 – 5x + 6

Answer 2

Answer:

The Sum of Two Roots of a Quadratic Equation is 5 and Sum of Their Cubes is 35

Step-by-step explanation:

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