Question

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

Answer 1

`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"`