INVERSE ROOT

Question

INVERSE ROOT

anonymous · Answer

Consider the polynomial$$ f(x)=17x^4+21x^3+60x^2+Ax+B$$. Suppose that for every root λ of f(x)=0, $$\frac{1}{λ}$$ is also a root of f(x)=0. What is the value of A+B?

anonymous · Answer

Details and assumptions
The roots may be complex-valued.

anonymous · Answer

Do you have given solutions?

anonymous · Answer

no i dont have but its between 0-1000

anonymous · Answer

@campbell_st @phi @TuringTest @shubhamsrg @sauravshakya @satellite73

anonymous · Answer

I got the two conditions:

$$\Large 17\lambda^4 +21\lambda^3 + 60 \lambda^2+ A \lambda + B =0 $$ After one longhand division and
$$\Large 17\lambda + 21 \lambda + 60 \lambda + \lambda A + B =0  $$
After the second

anonymous · Answer

how did you get part 2

shubhamsrg · Answer

Let roots be a,b, 1/a and 1/b
Product of roots = 1 = B/17

Sum of roots = -21/17 = 1/a + 1/b + a +b
Also, -A/17 = (a. b. 1/a) + (a. b. 1/b) + (a. 1/b. 1/a) + (b. 1/b. 1/a)
                   = b + a + 1/b + 1/a

You should be able to do now.

anonymous · Answer

yeh that does it,sufficient

anonymous · Answer

since -A/17=b+a+1/a+1/b
         -A/17=-21/17                  from the sum equation
           A=21
obviusly B=17
A+B=38