Need only handwritten solution only (not typed one). Consider a quadratic equation of the form x+bx+c 0, where b and c are rational numbers, Fill in the blanks in the following proof that if one solution is rational, then the othersolution is also rational.Proof: Supposex+bx+c=0 is any quadratic equation where b and care rational numbers, and suppose one solution ris rational. Call the other solutions. Thenx²+bx+c= (x-rx-s), Multiply out (x-r)(x-a) and set it equal to x² + bx+c to obtain x² bx+c=x² +-r+sSince and r✔are rationaland solve for a in terms of b and r to obtain aconclude that b-ris rational, and so sis rational.4Fosate coeftXand since differences of rational numbers are rational, wePS

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Answered: Consider a quadratic equation of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Due to the inflation three stores had to close in a mall: one athletic shoe store, one kid's clothing store, and one department store. The mall received 30 applications from store owners who applied to the mall to have their kid's clothing store to replace the closed kid's store. The mall also received 60 applications from athletic shoe store and department store owners who applied their store to replace the closed department and athletic shoe store. If X = the number of applications for a store, use this information to complete the table X 30 40 60 P(x) xP(x) O P(x)=.30, .30, .30; xP(x)=9,12, 18 O P(x)=.33, .33, .33; xP(x)=9.90, 13.20, 19.80 O P(x)=.03, .03, .03; xP(x)=.90,1.2,1.8
A new dormitory is to be constructed. There will be three types of rooms: single rooms which accommodate just 1 student per room, double rooms which accommodate 2 students per room, and triple rooms which accommodate 3 students per room. The dorm will contain 151 rooms and accommodate 262 students. Further, there will be 20 more double rooms than single rooms. Find the number of each type of room. There will be Blank 1. Calculate the answer by read surrounding text. single rooms. There will be Blank 2. Calculate the answer by read surrounding text. double rooms. There will be Blank 3. Calculate the answer by read surrounding text. triple rooms.
A homeowner wants to build, along his driveway, a garden surrounded by a fence. A rectangular garden has been enclosed along a side of a driveway. The enclosure is bordered by a length of fence along the driveway (a long side), another long side of fence, and two short sides of fence. The side along the driveway is labeled "$6 per foot" while the remaining three sides are labeled "$2 dollars per foot." If the garden is to be 1,800 square feet, and the fence along the driveway costs $6 per foot while on the other three sides it costs only $2 per foot, find the dimensions (in ft) that will minimize the cost. length along the driveway ft length perpendicular to the driveway ft Find the minimum cost (in dollars). $
A license plate used 2 digits followed by two letters. If the numbers 1 and 0 can not be used in the digits and the letter "O" can not be used as either letter, how many different license plates can be made?
Travis's carpet has an area of 180 square feet. He hires the CarpetPro carpet cleaning service, which is able to clean 9 square feet of his carpet every minute. Therefore, in the first minute, CarpetPro is able to clean 9 square feet of Travis's carpet (leaving 171 square feet remaining to be cleaned). In the second minute, the cleaner is again able to clean 9 square feet of carpet (leaving 162 square feet to be cleaned), etc. Which of the following functions expresses the number of square feet that still remain to be cleaned after t minutes from the time that the carpet cleaner began cleaning this carpet. A(t)=180−0.9t A(t)=180(0.1)t A(t)=180(0.9t) A(t)=180−9t A(t)=180−0.1t
During COVID-19 pandemic, Armondo helped his community by making tacos to give to hospital personnel. Some tacos had pork filling and some had beef filling. He made a total of 600 tacos, and made 60 more beef tacos than pork tacos. How many of each type of taco did he make?

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