Question

please help me to find the solution ​

Answer 1

Ur answer is here:

Let alpha=-2/root 3

Beta=root 3/4

Required polynomial is x^2-(alpha+beta)+alpha x beta

Put the value in Formula

U will get ur answer

Answer 2

So if any polynomial is p(x) and it's zeros are α and β then,

⇒ α + β = - 2/√3 + √3/4

⇒ α + β = - 2√3/3 + √3/4

⇒ α + β = (- 8√3 + 3√3)/12

⇒ α + β = - 5√3/3

Moreover, αβ = - 2/√3 × √3/4

⇒ αβ = - 1/2

∴ Sum of zeros = - 5√3/3 and Product of zeros = - 1/2

p(x) = k[ x² - (Sum of zeros)x + Product of zeros ]

→ p(x) = k( x² + 5√3x/3 - 1/2 )

Hence polynomial is k(x² + 5√3x/3 - 1/2) where k is any constant or real number.