How do you find the roots, real and imaginary, of #y=(x – 7 )^2-8x+4# using the quadratic formula?
1 Answer
or
Explanation:
If you would like to use the quadratic formula, you should expand your term first.
#y = (x-7)^2 - 8x + 4#
use the formula
#y = color(green)(x^2) color(brown)(- 2 * x * 7) + color(blue)(7^2) - 8x + 4#
#y = x^2 - 14x + 49 - 8x + 4#
#y = x^2 - 22x + 53#
Now, the quadratic formula is
#x = (- b +- sqrt(b^2 - 4ac)) / (2a)#
and in your case,
Thus, you can apply the formula:
#x = (22 +- sqrt((-22)^2 - 4 * 1 * 53) ) / 2 = (22 +- sqrt(484-212))/2#
# = (22 +- sqrt(272))/2 = (22 +- sqrt(16*17))/2 = (22 +- 4sqrt(17))/2#
You have two solutions:
#x = (22 + 4 sqrt(17))/2 ~~ 19.25#
or
#x = (22 - 4 sqrt(17))/2 ~~ 2.75#