How do you find the roots, real and imaginary, of y= 5x^2 - 6x - (2x+1)^2 using the quadratic formula?

1 Answer
Alan P.
Oct 20, 2017

Two Real roots at x=5+-sqrt(26)

Explanation:

y=5x^2-6x-(2x+1)^2

y=5x^2-6x-(4x^2+4x+1)

rarr y=color(red)1x^2color(blue)(-10)xcolor(green)(-1)

Applying the quadratic formula for roots:
color(white)("XXX")x=(-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(green)c))/(2color(red)a)
we have
color(white)("XXX")x=(-color(blue)((-10))+-sqrt(color(blue)((-10))^2-4xxcolor(red)1xxcolor(green)((-1))))/(2xxcolor(red)1)

color(white)("XXX")x=(10+-sqrt(100+4))/2

color(white)("XXX")x=5+-sqrt(104)/2

color(white)("XXX")x=5+-sqrt(26)

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