Question

In a triangle $ABC,\angle C={90}^0.a,b$ are the sides and $c$ is the hypotenuse of a right angled triangle, then the equation whose roots are $\tan A$ and $\tan B$ is

• A. $ab{x}^2+c^{2}x+ab=0$
• B. $ab{x}^2+c^{2}x-ab=0$
• C. $ab{x}^2-c^{2}x-ab=0$
• D. $ab{x}^2-c^{2}x+ab=0$

Answer 1

Answer: (D)

$ab{x}^2-c^{2}x+ab=0$

In right angled $△ABC$

$a^2+b^2=c^2$
so $\tan A=\frac{a}{b}$
and $\tan B=\frac{b}{a}$
$\tan A$ $+$ $\tan B$ $=$ $\frac{a}{b}+\frac{b}{a}=\frac{a^2+b^2}{ab}=\frac{c^2}{ab}$
$\tan A$ $\tan B$ $=$ $1$
So equation is $x^2-(\tan A+\tan B)x+\tan A\tan B=0$
$ab{x}^2-c^{2}x+ab=0$