20x⁴+21x³-400x²-21x+20=0

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