Question

Solve the function.

x³ + 2x² - 5x + 12 = 0
HEY GUYS I RLLY NEED HELP I DONT KNOW WHAT “?” IS! PLS PLS

Answer 1

Answer: x=-4, x=1±√2i

Explanation:

`x^3+2x^2-5x+12=0\\x^3+2x^2+2x^2-2x^2-5x+12=0\\(x^3+4x^2)-(2x^2+5x-12)=0\\(x^2*(x+4))-(2x^2+5x+3x-3x-12)=0\\x^2*(x+4)-((2x^2+8x)-(3x+12))=0\\x^2*(x+4)-(2x*(x+4)-3*(x+4))=0\\x^2*(x+4)-(x+4)*(2x-3)=0\\(x+4)*(x^2-(2x-3))=0\\(x+4)*(x^2-2x+3)=0\\x+4=0\\x=-4\\`

`\displaystyle\\x^2-2x+3=0\\a=1\ \ \ \ b=-2\ \ \ \ c=3\\D=b^2-4ac\\D=(-2)^2-4*1*3\\D=4-12\\D=-8\\√(D)=√(-8) \\√(D)=√(-1*4*2) \\√(D)=√(-1)*√(4)*√(2) \\ √(D)=2√(2)i\\\\`

`\displaystyle\\x=(-bб√(D) )/(2a) \\\\x=(-(-2)б2√(2)i )/(2*1) \\\\x=(2б2√(2)i )/(2) \\\\x=(2*(1б√(2)i) )/(2)\\ x=1б√(2)i`