Homework Help Question & Answers

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

How do you find the roots, real and imaginary, of #y=(x/5-5)(-3x-2)# using the quadratic formula?
0 0
Next > < Previous
ReportAnswer #1

See a solution process below:

Explanation:

First, we need to write this equation in standard form:

#y = (color(red)(x/5) - color(red)(5))(color(blue)(-3x) - color(blue)(2))# becomes:

#y = -(color(red)(x/5) xx color(blue)(3x)) - (color(red)(x/5) xx color(blue)(2)) + (color(red)(5) xx color(blue)(3x)) + (color(red)(5) xx color(blue)(2))#

#y = -3/5x^2 - 2/5x + 15x + 10#

#y = -3/5x^2 - 2/5x + (5/5 * 15)x + 10#

#y = -3/5x^2 - 2/5x + 75/5x + 10#

#y = -3/5x^2 + 73/5x + 10#

We can now use the quadratic equation to solve the equation. The quadratic formula states:

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)))/(2color(red)(a))#

Substituting:

#color(red)(-3/5)# for #color(red)(a)#

#color(blue)(73/5)# for #color(blue)(b)#

#color(green)(10)# for #color(green)(c)# gives:

#x = (-color(blue)(73/5) +- sqrt(color(blue)(73/5)^2 - (4 * color(red)(-3/5) * color(green)(10))))/(2 * color(red)(-3/5))#

#x = (-color(blue)(73/5) +- sqrt(5329/25 - (-120/5)))/(-6/5)#

#x = (-color(blue)(73/5) +- sqrt(5329/25 - (5/5 * -120/5)))/(-6/5)#

#x = (-color(blue)(73/5) +- sqrt(5329/25 - (-600/25)))/(-6/5)#

#x = (-color(blue)(73/5) +- sqrt(5329/25 + 600/25))/(-6/5)#

#x = (-color(blue)(73/5) +- sqrt(5929/25))/(-6/5)#

#x = (-color(blue)(73/5) + 77/5)/(-6/5)# and #x = (-color(blue)(73/5) - 77/5)/(-6/5)#

#x = (4/5)/(-6/5)# and #x = (-150/5)/(-6/5)#

#x = -(4 * 5)/(5 * 6)# and #x = (150 * 5)/(5 * 6)#

#x = -4/6# and #x = (150)/(6)#

#x = -2/3# and #x = 25#

answered by: smendyka
Know the answer?
Add Answer of:
How do you find the roots, real and imaginary, of #y=(x/5-5)(-3x-2)# using the quadratic formula?
Your Answer: Your Name: What's your source?
Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Free Homework App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
Share Your Knowledge

Post an Article
Post an Answer
Post a Question with Answer

Self-promotion: Authors have the chance of a link back to their own personal blogs or social media profile pages.