Question

Розв’язати рівняння x4 – 9x3 + 21x2 + x – 30 = 0. ​

Answer 1

$\displaystyle x^4-9x^3+21x^2+x-30=0\\x^4+x^3-10x^3-10x^2+31x^2+31x-30x-30=0\\x^3(x+1)-10x^2(x+1)+31x(x+1)-30(x+1)=0\\(x+1)(x^3-10x^2+31x-30)=0\\(x+1)(x^3-2x^2-8x^2+16x+15x-30)=0\\(x+1)(x^2(x-2)-8x(x-2)+15(x-2))=0\\(x+1)(x-2)(x^2-8x+15)=0\\(x+1)(x-2)(x^2-3x-5x+15)=0\\(x+1)(x-2)(x(x-3)-5(x-3))=0\\(x+1)(x-2)(x-3)(x-5)=0\\x+1=0,x-2=0,x-3=0,x-5=0\\x_1=-1,x_2=2,x_3=3,x_4=5$