# Form the quadratic equation whose roots are:

1 view

Form the quadratic equation whose roots are:

(i) √3 and 3√3

(ii) 2 + √5  and  2 - √5

answered Feb 9 by (-1,946 points)

(i) Let α, β be the roots of  the required quadratic equation :

Then, α = √3 and β = 3√3

α + β  = √3 + 3√3  and αβ = √3 × 3√3

∴  α + β = 4√3  and  αβ = 9

x2 – (α + β)x +  αβ = 0

⇒ x2 - 4√3x + 9  = 0

(ii) Let α, β be the given roots.

Then   α = 2 + √5  and  β = 2 - √5

α + β = 2 + √5 + 2 - √5 = 4

and  αβ = (2 + √5)(2 - √5)

⇒ α + β = 4 and αβ = (2)2 -  (√5)2

⇒ α + β  = 4 and αβ = 4 - 5

⇒ α + β = 4 and  αβ  = - 1

x2  - (α + β)x  +  αβ = 0

⇒  x2  – 4x – 1 = 0