Question

If the sides of a triangle are the roots of the equation $x^3-2x^2-x-16=0$,

then the product of the in-radius and circum- radius of the triangle is

• A. $3$
• B. $6$
• C. $4$
• D. $2$

Answer 1

Answer: (C)

$4$

Let the roots and sides of triangle be $a,b,c$

$\Rightarrow a+b+c=2$ and $abc=16$

$rR=\frac{\Delta }{s}\times \frac{abc}{4\Delta }=\frac{abc}{4s}$

$=\frac{abc}{2(a+b+c)}$

$=\frac{16}{4}=4$