How do you find the roots, real and imaginary, of #y= 5x^2 - 245 # using the quadratic formula?

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Answer 1 · 2017-10-26T16:48:08

See a solution process below:

First, we can rewrite this equation as:

#y = 5x^2 + 0x - 245#

To find the roots we need to set the right side of the equation equal to #0# and solve for #x#:

#5x^2 + 0x - 245 = 0#

We can now use the quadratic equation to solve this problem:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(5)# for #color(red)(a)#

#color(blue)(0)# for #color(blue)(b)#

#color(green)(-245)# for #color(green)(c)# gives:

#x = (-color(blue)(0) +- sqrt(color(blue)(0)^2 - (4 * color(red)(5) * color(green)(-245))))/(2 * color(red)(5))#

#x = +- sqrt(0 - (-4900))/10#

#x = +- sqrt(0 + 4900)/10#

#x = +- sqrt(4900)/10#

#x = -70/10# and #x = 70/10#

#x = -7# and #x = 7#