Question

If α + β = –1 and α3 + β3 = –37, then the quadratic equation whose roots are α and β, is

Answer 1

Answer:

answer is alpha=3,beeta=-4

Answer 2

The required equation is x²+ x –12 = 0  

Given:

α + β = –1 and α³ + β³ = –37

To find:

Find the quadratic equation whose roots are α and β, is

Solution:

Given α³+β³ = –37

   and α + β = –1  ----- (1)

From the algebraic identity  (a+b)³ = a³+b³+3ab(a+b)  

⇒  (α+β)³ = α³+β³ + 3αβ (α+β)  

⇒  ( –1 )³  =  –37  + 3αβ (–1 )  

⇒ –1 + 37 = – 3αβ

⇒  3αβ  = – 36

⇒ αβ  = – 12 ------ (2)

Note:

The formula for a Quadratic Equation with sum of roots and product of roots is given by

          x² – (sum of roots)x + product of roots = 0

Given α and β are roots of Quadratic Equation

Then the required equation is  x²– (α + β)x + αβ = 0  

⇒ x²– (–1)x + (–12) = 0  

⇒  x²+ x –12 = 0  

The required equation is x²+ x –12 = 0

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