Question

X^3+7x^2+13x+4=0 Show all work

Answer 1

`\displaystyle\\ x^3+7x^2+13x+4=0\\\\ x^3+\underbrace{4x^2+3x^2}_(7x^2)+\underbrace{12x+x}_(13x)+4=0\\\\ (x^3+4x^2) + (3x^2 + 12x)+(x+4)=0\\\\ x^2(x+4)+3x(x+4)+(x+4)=0\\\\ (x+4)(x^2 + 3x +1)=0\\\\ x+4 = 0~~~\Longrightarrow~~~\boxed{x_1 = -4}\\\\ x^2 + 3x +1=0\\\\ x_(23)= (-b\pm √(b^2-4ac) )/(2a)= (-3\pm √(3^2-4\cdot 1 \cdot 1) )/(2\cdot 1)= (-3\pm √(5) )/(2)\\\\ \boxed{x_2 = (-3-√(5) )/(2)}\\\\ \boxed{x_3 = (-3+√(5) )/(2)}`