Mathematics

Write complete, concise responses to the following problems. Show ALL . Subfect, Mathematics relevant work on any calculations, and be sure to explain what you are doing. Finally, please staple this sheet to the top of your work.
Academic Level Bachelor
Paper deta. 1. Given any quadratic equation of the form ax^2+bx +c= 0, it is always possible to find its solutions. The purpose of this problem is to explore the solutions in greater detail. It tums out that the sum of the solutions to any quadratic equation is equal to “-1,/,. while the product of the solutions is equal to “c/a.. For example, fro the quadratic equation 3x^2- 8x+4=0(the coefficients are a=3, b=-8, and c=4), the solutions are x=2/3 and x=2. The sum is 2+2/3=8/3( the opposite of the ratio “b” to ‘a.), while the product is 2(2/3)=4/3(the
Fine the quadratic equation whose solutions have a sum of 3/4 and a product of 1/8. To get started, you will need to figure out the values of the coefficients a,b, and c. Then show that the resulting equation works by solving the equation, followed by checking that the solutions have the indicated sum and product. Your final equation should have coefficients that are integers, with no common factors between them all(other than 1).
2p.uGiovseen oainthyifunction(and possibly certain domain restrictions), it is possible to find the inverse of the function. The rp is pwronblienmveirssetolohoekfaoiltfou,n,icntgioin ssatnhoatthaerreetheir own inverses. For example, 0(x).-x is it’swn o inverse, while 1,9 it.ss o T xample of a function that is it’s ovvn inverse. MM. 9+39/-1
Explain what it means for M(x) to 2+ 9/ own inverse, both algebraically and graphically. Please include a domain/range discussion as well.

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