Quadratic Equation------
if the roots of ax^2+x+b=0 be real and unequal ,show that the roots of (x^2+1)/x =4√ab are imaginary.

Question

Quadratic Equation------
if the roots of ax^2+x+b=0 be real and unequal ,show that the roots of (x^2+1)/x =4√ab are imaginary.

wwe123 · Answer

if the roots of ax^2+x+b=0 be real and unequal ,show that the roots of (x^2+1)/x =4√ab are imaginary roots.

hartnn · Answer

since roots of ax^2+x+b=0 be real,
we can say 
1-4ab>0
got this ?

wwe123 · Answer

yes

hartnn · Answer

now, x^2 - 4$\sqrt{ab}$x+1=0
has, 
determinant as 
16ab-4
ok?

wwe123 · Answer

i do not understand

hartnn · Answer

which part ? 
did u get how i got 1-4ab>0    ??

wwe123 · Answer

yes

hartnn · Answer

how did i get it ?

wwe123 · Answer

this part 
x^2 - 4ab√x+1=0
has, 
determinant as 
16ab-4
ok?

hartnn · Answer

i meant u know how to find determinant of a quadratic equation ?

wwe123 · Answer

yes i know how .......

hartnn · Answer

so find the determinant of 2nd equation.
x^2 - 4$\sqrt{ab}$x+1=0

hartnn · Answer

or u did not get how i got that equation^ ?

hartnn · Answer

(x^2+1)/x =4√ab 
 (x^2+1) =4√ab x
 x^2+1 -4√ab  x=0

wwe123 · Answer

is 4ab >-1 is this correct

hartnn · Answer

1-4ab>0 1>4ab 4ab<1 16ab<4 16ab-4<0 determinant is negative-->roots are imaginary.