Successive Cubic Rational Root

Algebra Level pending

Let f ( x ) = a x 3 + b x 2 + c x + d f(x) = ax^3 + bx^2 + cx + d where c c and a a and f ( 1 ) f(1) are successive positive integers, or 0 < c < a = 2 k < f ( 1 ) 0 < c < a=2k < f(1) for some integer k k . Find d d such that f ( x ) = ( a x + d ) [ x 2 + ( c − a d ) x + d ] f(x) = (ax + d)[x^2 + (c-ad)x +d] .


The answer is 1.

Frank Giordano by Frank Giordano , 57, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Frank Giordano
Sep 21, 2016

Teachers: this cubic is useful if you want to easily create a cubic that has two coefficients of your choosing and rational root x = − 1 / ( 2 k ) x = -1/(2k) . Just pick 3 successive integers, remember a a is even and d = 1 d = 1 and b = − c b = -c .

this facebook video explains the Game of G-filtered Polycules for Cubics; leave a comment.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

get the latest version of "G-filtered Polycules" here: https://www.facebook.com/groups/factorthis/

Frank Giordano - 4 years, 7 months ago

lol, just noticed, via inspection of the problem, d squared equals d implies d equals one.

Frank Giordano - 3 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...