y-x-5-ax-4-bx-3-cx-2-dx-e-If-we-let-x-t-h-can-we-find-h-in-terms-of-a-b-c-d-e-such-that-y-t-R-t-2-pt-q-t-2-s-this-means-two-roots-are-of-opposite-sign-of-course-its-possible-by-shifting-the

Question Number 67819 by ajfour last updated on 31/Aug/19

y = x^{5} + {a x}^{4} + {b x}^{3} + {c x}^{2} + d x + e

I f w e l e t x = t + h

c a n w e f i n d h i n t e r m s o f a, b, c, d, e

s u c h t h a t

y = (t + R) (t^{2} + p t + q) (t^{2} + s)

t h i s m e a n s t w o r o o t s a r e o f

o p p o s i t e s i g n, o f c o u r s e i t s

p o s s i b l e b y s h i f t i n g t h e c u r v e

a l o n g x, b u t c a n w e f i n d t h e

s h i f t h ?

Commented by TawaTawa last updated on 31/Aug/19

Weldone sir on the evetyday trial . It will be fruitful sir .

God bless you sir