Find-the-number-of-quadratic-equations-having-real-roots-and-which-do-not-change-by-squaring-their-roots-

Question Number 2191 by lakshaysethi039 last updated on 07/Nov/15

F i n d t h e n u m b e r o f q u a d r a t i c e q u a t i o n s h a v i n g r e a l r o o t s

a n d w h i c h d o n o t c h a n g e b y s q u a r i n g t h e i r r o o t s .

Answered by prakash jain last updated on 07/Nov/15

Eq : {a x}^{2} + b x + c = 0

Let roots be α, β

Equation remain the same after roots are

squared so same equation gives roots α^{2} and β^{2} .

α = α^{2}, β = β^{2}

α = 0, 1 β = 0, 1

roots = (0, 0) \lor (1, 0) \lor (1, 1)

Three equations are

x^{2} = 0

x^{2} - x = 0

x^{2} - 2 x + 1 = 0