Question

If $a,b,c$ be the sides of $TriangleABC$ and equations $a{x}^2+bx+c=0$ and $5x^2+12x+13=0$ have a common root, then $\angle C$ is

• A. ${60}^{\circ }$
• B. ${90}^{\circ }$
• C. ${120}^{\circ }$
• D. ${45}^{\circ }$
  

Answer 1

The correct option is B ${90}^{\circ }$


Solution : $5x^2+12x+13=0$ have complex roots i.e. both root will be common to $a{x}^2+bx+c=0$
$\frac{a}{5}=\frac{b}{12}=\frac{c}{13}=k$
$\angle C={90}^{\circ }$