Question

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is 

A. x² + 4 = 0 

B. x² – 4 = 0 

C. 4x² – 1 = 0 

D. x² – 2 = 0

Answer 1

Let Root of an equation = α = 2 

Sum of the roots = α + β = 0, where α and β are two roots of the equation 

β = – 2 

α β = 2 x – 2 = – 4 

the general equation is of the form 

x² + (sum of the roots)x + product of the roots = 0 

x² – 4 = 0 is the required equation