Question

If the sides of a triangle are the roots of x³ –2x² –x – 16 = 0 then product of the in-radius and circum-radius is-

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (B)

4

Answer 2

Let the sides of the D be a, b, c. Since a, b, c are roots of

x³ – 2x² + x – 16 = 0

\ Sum of the roots a + b + c = 2 Ž 2S = 2 i.e. S = 1

Where S is the semi-perimeter of the D. Product of the roots i.e. a. b. c = 16

\ R. r = $\frac{abc}{4\Delta}$. $\frac{\Delta}{S}$= $\frac{abc}{4S}$= 4