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If the roots of the equation (a-b)x² + (b-c)x + (c-a) = 0 are equal , the prove 2a=b+c.

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Solve the equation:-a/x-b + b/x-a = 2Answer:-x=a+b or a+b/2[nOTE:-Please give all the solution possible on this Question as i am not able to solve in my way..

Draw an ogive for the following frequency distribution. Use your ogive to estimate:Marsks    : 0 - 9  10 - 19  20 - 29  30 - 39  40 - 49  50 - 59  60 - 69  70 -79  80 -89            No.ofStudents :    5        9          16        22         26        18        11         6          4                90 - 99                    3(I) The Median, (2) The number of students who obtained more than 75% marks.   (use square paper to solve this question).2.  In a public collection towards the erections of a memorial, 1000 people contributed  sums of money varying from Rs.1 to Rs. 100 ( in units of Rs. 1). The following table gives the frequency distribution of contribution:Contribution        No. of people.            Contribution              No. of people(in Rs.)                                                  (Rs.)  1 - 10                        30                      51 - 60                            18011  - 20                        60                     61 - 70                            14021 -  30                        80                     71 - 80                            7031 -  40                       170                    81 - 90                            4041 -  50                       200                    91 - 100                          30Using a suitable scale, draw on graph paper an ogive (cumulative frequency graph)and use it to answer the following:(1) Estimate the median.(2) If it is agreed to allow only those who contributed Rs. 45 or more to attend the unveiling ceremony, what percentage would attend?

The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm,find the distance between their centres.

A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208m² , fnd the width of the footpath.(Please give the procedure.)

The compound interest calculated yearly on a certain sum of money for the second year is Rs. 880 and for the third year it is Rs. 968. Calculate the rate of interest and the sum of money.

Draw an ogive for the following frequency distribution. Use your ogive to estimate:Marsks    : 0 - 9  10 - 19  20 - 29  30 - 39  40 - 49  50 - 59  60 - 69  70 -79  80 -89             No.ofStudents :    5        9          16        22         26        18        11         6          4                90 - 99                    3(I) The Median, (2) The number of students who obtained more than 75% marks.   (use square paper to solve this question).2.  In a public collection towards the erections of a memorial, 1000 people contributed  sums of money varying from Rs.1 to Rs. 100 ( in units of Rs. 1). The following table gives the frequency distribution of contribution:Contribution        No. of people.            Contribution              No. of people (in Rs.)                                                  (Rs.)   1 - 10                        30                      51 - 60                            18011  - 20                        60                     61 - 70                            14021 -  30                        80                     71 - 80                            7031 -  40                       170                    81 - 90                            4041 -  50                       200                    91 - 100                          30Using a suitable scale, draw on graph paper an ogive (cumulative frequency graph)and use it to answer the following:(1) Estimate the median.(2) If it is agreed to allow only those who contributed Rs. 45 or more to attend the unveiling ceremony, what percentage would attend?

Prove that any four vertices of a regular pentagon are concyclic(lies on the same circle).