Question

Comment upon the nature of the roots without solving

1.). X^{​​​​​​2} - as - b^{​​​​​​2} = 0

When I solved the equation I got the roots as

A^{​​​​​​2} + 4b²

But the answer is given as the roots are positive so it is real and unequal how is it? And why is it?

A's value can be a negative no also like a= -3

So how can this be possible?

Answer 1

X^2 -aX-b^2=0
product of the roots=c/a
=-b^2/1
=-b^2(negative)
if the product of roots is negative,one of roots should be NEGATIVE
when we check discriminant it is clear that the roots are unequal and real

but one of roots is negative