Question

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $l{x}^2+mx+n=0$ then

• A. $l^2-m^2+2ln=0$
• B. $l^2+m^2+2ln=0$
• C. $l^2-m^2-2ln=0$
• D. $l^2+m^2-2ln=0$

Answer 1

The correct option is A $l^2-m^2+2ln=0$

$\sin \alpha$ and $\cos \alpha$ are the roots of the equation $l{x}^2+mx+n=0$

So, $\sin \alpha +\cos \alpha =-\frac{m}{l}$ and $\sin \alpha \cos \alpha =\frac{n}{l}$

Now squaring the above equation $\left(1\right)$

$\Rightarrow$ ${\sin }^2\alpha +$ ${\cos }^2\alpha +$ $2\sin \alpha \times \cos \alpha =1+2$ $\sin \alpha \times \cos \alpha$

Put the values from equation $1$ and equation $2$,

$\Rightarrow 1+\frac{2n}{l}=\frac{m^2}{l^2}$ or $l^2-m^2+2ln=0$

Hence, option A is correct.