Question

If the equation $a{x}^2+bx+c=0$ and $5x^2+12x+13=0$ have a common root, where a, b and c are the sides of a triangle $ABC$ then

• A. $\Delta ABC$ is acute angled
• B. $\Delta ABC$ is right angled
• C. $\Delta ABC$ is isosceles
• D. $\Delta ABC$ is right angled isosceles

Answer 1

The correct option is B $\Delta ABC$ is right angled

If one equation has imaginary roots and it has a common root with other equation then ratio of respective coefficients are equal

$\Rightarrow \frac{a}{5}=\frac{b}{12}=\frac{c}{13}$

$\Rightarrow a=5k;b=12k;c=13k$. Where 'k' is some constant

As $c^2=a^2+b^2$, it is a right angled triangle