Question

Diminish by 3 the roots of the equation
$x 5 -4 x 4 + 3x 3 - 4x + 6 = 0$
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Answer 1

x4(x-4)+x(3x2-4)

(x4+x)(3x2-4x)

x4+x=0

2x4=0

x4=2

3x3-4x

x2=1

Answer 2

Answer:

F(x)=$x^5 - 4x^4 +3x^3 -4x^2 + 6=0$

Here, x is the root of the following eq.

New root is y=x$-3$

$= > x=y-3$

Upon substitution and conversion to F(y) is

F(y)= $(y-3)^5 - 4(y-3)^4 +3(y-3)^3 - 4(y-3)^2 +6 = 0$

This upon solving creates the polynomial with a diminishing root by 3.

F(y)= $y^5+11y^4+78y^3+219y^2+311y-60=0$

#SPJ3