Question

If $a\in R^{+}\&b\in R$, then the equation $x^2-abx-a^2=0$ has

• A. One positive and one negative root
• B. Both positive
• C. Both negative
• D. Can't say

Answer 1

The correct option is A

One positive and one negative root

We know that, for the equation, $a{x}^2+bx+c=0,$ product of the roots $=\frac{c}{a}$
So, for the equation, $x^2-abx-a^2=0,$ product of the roots $=-a^2$
Which is negative as $a\in R^{+}$
Since, product of roots is negative, the roots must be of opposite signs.