Question

If p and q are positive then the roots of the equation $x^2-px-q=0$ are-

• A. imaginary
• B. real & both positive
• C. real & both negative
• D. real & of opposite sign

Answer 1

The correct option is D real & of opposite sign

Quadratic is : $x^2-px-q=0$

$D=b^2-xac$

$=(-p{)}^2-4(1\left)\right(-q)$

$=p^2+4q>o(asp,q>o)$

$\Rightarrow$ roots are real.

Let roots $=\alpha ,\beta$

$\Rightarrow \alpha +\beta =p,\alpha \beta =-q$

at $\alpha \beta =-q<0$

$\Rightarrow \alpha$ and $\beta$ are of opposite sign.