Question

If alpha,beta the roots of the equation ax^2+2bx+c=0and alpha+h ,beta+h are the roots of the equation Ax^2+2Bx+C=0,then​

Answer 1

for ax2+2bx+c=0 2+2bx+c=0 roots are αα and ββ

difference of the roots = α−β=4b2−4aca2−−−−−−√α−β=4b2−4aca2

for Ax2+2Bx+C=0Ax2+2Bx+C=0 roots areα+δα+δand β+δβ+δ

difference of the roots =α−β=4B2−4ACA2−−−−−−−√α−β=4B2−4ACA2

from the above we get that

4b2−4aca2−−−−−−√=α−β4b2−4aca2=α−β

4B2−4ACA2−−−−−−−√=α−β4B2−4ACA2=α−β

b2−a