Let a, b, c, p, q be real numbers. Suppose, , are the roots of the equation x^2+2 p x+q=0 and , 1 are the roots of the equation a x^2+2 b x+c=0 , where ^2 -1,0,1 . Statement 1 (p^2-q ) (b^2-a c ) 0 . Statement 2 b p a or c q a .

Step-by-step solution

Given, and are the roots of x^2+2 p x+q=0 . array rlrl & & + & =-2 p and & & =q array and 1 are the roots of a x^2+2 b x+c=0 and + 1 = -2 b a and = c a Now, aligned (p^2-q ) (b^2-a c ) & = [ ( + -2 )^2- ] [ ( + 1 2 )^2- ] a^2 & = ( - )^2 16 ( - 1 )^2 a^2 0 aligned Statement 1 is true. array ll Again now, & p a=- ( + 2 ) a=- a 2 ( + ) and & b=- a 2 ( + 1 ) & p a b + 1 + & 1 & ^2 -1,0,1 , correct. Similarly, if & c q x & a a ( - 1 ) 0 array array ll & 0 and - 1 0 & -1,0,1 array Statement 2 is true. Both Statement 1 a