Question

Find a quadratic equation whose one of the root is 2 and whose sum of the roots of zero

Answer 1

Let α and β are the roots of the required equation.
Now, α = 2
also sum of roots = α + β = 0 ⇒ β = -2
now, αβ = product of roots = (2) (-2) = -4
Now, the required quadratic equation is given by
x^2 - [ α + β ] x + αβ = 0
that is x^2 - 0x + (-4) = 0
x^2 - 4 = 0