Choko was walking the streets of PussyCat Ville when he found a chipmunk. The chipmunk said if x^3+5x^2+12x+32 are a polynomial with roots r, s and t. Can you find a 3rd degree polynomial with roots 1/r, 1/s and 1/t?
DM me to submit answer. First person to submit right also gets a Captain Rescue!!!
Greetings! Thank you for trying the math question.
The answer is the following:
Let f(x) be the function x^3+5x^2+12x+32. Define a new function F(1/x)=f(x). Then F(1/r)=f(r)=0, and the same follows with r, s and t. So, F(1/r) has roots 1/r, 1/s and 1/t.
To find F, we plug in 1/x as r, this yields F(1/1/x)=F(x)=f(1/x)=1/x^3+5/x^2+12/x+32.
We multiply by x^3 to get a third-degree polynomial.
I accepted any constant multiplied by this polynomial. For example: x^3+3/8x^2+5/32x+1/32 was accepted!
For those of you who got it right, I've sent you your prize. for thoses that got it wrong, I sent 1 CHOKO anyway!!!