20x⁴+21x³-400x²-21x+20=0

Question

20x⁴+21x³-400x²-21x+20=0

Answer 1

20x⁴+21x³-400x²-21x+20=0
P1(x)=20x⁴+21x³-400x²-21x+20   

P1(4) =0  ⇒  x=4 - корень уравнения  20x⁴+21x³-400x²-21x+20=0

20x⁴+21x³-400x²-21x+20=(x-4)(20x³+101x²+4x-5)

P2(x)=(20x³+101x²+4x-5)
 P2(-5) =0  x=-5 -  корень уравнения (20x³+101x²+4x-5)=0


(20x³+101x²+4x-5)=(x+5)(20x²+x-1) ⇒
20x⁴+21x³-400x²-21x+20=(x-4)(20x³+101x²+4x-5)=(x-4)(x+5)(20x²+x-1)


(20x²+x-1)=0 

x1=(-1-√(1+80))/40=-1/4     x2=(-1+√(1+80))/40=1/5   

20x⁴+21x³-400x²-21x+20=20(x-4)(x+5)(x-1/5)(x+1/4)

x1=4   x2= -5  x3=1/5   x4= -1/4

Comments

что такое Р1