Question

Find the polynomial whose zeros are root 3 by 2 and minus root 3 by 2

Answer 1

Let α=√3/2
β=-√3/2
When roots are given, a quadratic equation is always
x²+(α+β)x+αβ
Substituting values,
x²+(√3/2-√3/2)x+(√3/2)×(-√3/2)
x²-3/4

Answer 2

x² - ( X + Y ) + XY ---------- 1

so substituting the roots in 1 we get

4x² +  0x  -  3 = 0