if one root of the equation (l-m)x^2 + lx +1 =0 be the double of the other and if l - Maths - Quadratic Equations

Question

if one root of the equation (l-m)x^2 + lx +1 =0 be the double of
the other and if l is real show that m<_9/8

Lovina Kansal · Accepted Answer

Dear student
We have,(l-m)x2+lx+1=0Let the root of the above polynomial be r
 Then according to question other root is double of the one root
 So, the other root is 2rr+2r=-ll-m⇒3r=-ll-m⇒r=-l3l-m   
(1)and r
2r=1l-m⇒2r2=1l-m⇒r2=12l-m⇒l29l-m2=12l-m   (from 1)⇒2l2=9l-m⇒2l2-9l+9m=0For l to be real, the discriminant is non- negative81≥8×9m⇒m≤98Hence Proved
Regards

if one root of the equation (l-m)x^2 + lx +1 =0 be the double of the other and if l is real show that m<_9/8