Question

If the sum of the roots of an equation is –2 and the sum of their cubes is 82, then equation is
​

Answer 1

$\huge\boxed{Answer}$

⇒  Let α and β are roots of the required equation.

⇒  α+β=2                   [ Given ]         ---- ( 1 )

⇒  α3+β3=98

⇒  (α+β)(α2−αβ+β2)=98

⇒  2(α2+2αβ+β2−3αβ)=98          [ Using ( 1 ) ]

⇒  [(α+β)2−3αβ]=49

⇒  (2)2−3αβ=49

⇒  4−3αβ=49

⇒  3αβ=−45

∴  αβ=−15                         ----- ( 2 )

New equation,

⇒  x2−(α+β)x+(αβ)=0

Using ( 1 ) and ( 2 ),

⇒  x2−2x−15=0

$\huge\mathfrak\red{itz\:jyotsana☺}$