How do you find the roots, real and imaginary, of #y= 3x^2 - 9x +26 - (x-5)^2 # using the quadratic formula?

1 Answer
Dec 24, 2017

Answer:

#x=-1/2+-1/2sqrt7i#

Explanation:

#"expand "(2x-5)^2" using FOIL and arrange in "color(blue)"standard form"#

#•color(white)(x)ax^2+bx+c color(white)(x);a!=0#

#"using the "color(blue)"quadratic formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(x=(-b+-sqrt(b^2-4ac))/(2a))color(white)(2/2)|)))#

#y=3x^2-9x+26-(x^2-10x+25)#

#color(white)(y)=3x^2-9x+26-x^2+10x-25#

#color(white)(y)=2x^2+x+1#

#"with "a=2,b=1,c=1#

#x=(-1+-sqrt(1-8))/2#

#color(white)(x)=(-1+-sqrt7i)/2#

#rArrx=-1/2+-1/2sqrt7ilarrcolor(red)"complex roots"#