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A1a) k < or equal 1 or k > or equal 8, k is not equal 0; 7 A1b) 2p^3 = q^2 - q^3 Q2) The curve y = ab^x passes through the points (0,5) and (2/3,5/4). Find the positive value of a and of b. A2) a = 5, b = 1/8 Q3)a) Find the non-zero value of k for which equation 3x^2 + 2kx - k = 0 has i) 2 equal roots ii) 2 real roots, one of which is the reciprocal of the other. iii) 2 real roots, one of which is twice the other. A3a) i) -3 ii) -3 iii) -27/8 Q3b) Find the value of k for which the equation 4(x + 1)(x - 4) = k has roots which differ by 8 A3b) 39 Q4) The equation 2x^2 + 7x + a = 0 has roots A and B and 4x^2 + bx + 16 =0 has roots A^2 and B^2. Calculate the possible values of a and b. A4) a = 4, b = -33, or a = -4, b = -65 Q5) The roots of a quadratic equation 3x^2 - square-root24 X - 2 = 0 are m and n where m > n. Find the value of 4/m - 2/n in the form square root a - square root b A5) square root 108 - square root 6 Sponsors:    8th April 2012, 05:00 PM #2 (permalink) Experienced SGClubber    Posts: 2,404 Join Date: Jul 2009 Likes: 0 Liked 211 Times in 174 Posts Gender: Re: Discriminants and roots problem Tweet Are you trying to get someone do your homework here? __________________ White Group Mathematics Free A Level H2 Maths Resource Site    8th April 2012, 06:12 PM #3 (permalink) New SGClubber Posts: 28 Join Date: Oct 2010 Likes: 4 Liked 2 Times in 2 Posts Gender: Re: Discriminants and roots problem Tweet dude, these are very simple sec 3 A-maths questions. If you're a student please attempt to read through the examples in your textbook and then try out the questions. If you just want free answers you will never ace your tests.    8th April 2012, 06:59 PM #4 (permalink) Addicted SGClubber  Posts: 518 Join Date: Mar 2012 Likes: 1 Liked 17 Times in 16 Posts Gender: Re: Discriminants and roots problem Tweet You sure you can't solve them? They're really simple ! :/    8th April 2012, 07:19 PM #5 (permalink) Experienced SGClubber  Posts: 1,423 Join Date: Feb 2012 Likes: 53 Liked 53 Times in 51 Posts Gender: Re: Discriminants and roots problem Tweet TS has been exposed~ Do it yourself before asking for help. __________________ -Within the Darkness- "I will take every morsel of light from this world, so that you have nowhere to run to but the shadows. And when I find you, they will bring you bound by chains into my chambers where I shall look into your eyes﻿ before I rip you from your futile existence. Your blood shall rain upon my throne of darkness, and seep into the cracks of a world once filled with light."    8th April 2012, 11:24 PM #6 (permalink) Cool SGClubber  Posts: 259 Join Date: Dec 2009 Likes: 10 Liked 7 Times in 6 Posts Gender: Re: Discriminants and roots problem Tweet Originally Posted by whitecorp Are you trying to get someone do your homework here? No, I am only asking for guides dude, these are very simple sec 3 A-maths questions. If you're a student please attempt to read through the examples in your textbook and then try out the questions. If you just want free answers you will never ace your tests. Originally Posted by KeaneLJC You sure you can't solve them? They're really simple ! :/ If it is simple, I wouldn't have wasted my time to post these questions already, I started A-Maths in Sec 5, inside the textbook, the examples only show basic questions, that is why I post these questions Originally Posted by themightyblue TS has been exposed~ Do it yourself before asking for help. I tried for days, I can't get the answer, Do you mean I should also post the answer that I attempted?    9th April 2012, 02:04 AM #7 (permalink) Experienced SGClubber    Posts: 2,404 Join Date: Jul 2009 Likes: 0 Liked 211 Times in 174 Posts Gender: Re: Discriminants and roots problem Tweet Posting a long list of questions and their answers is not the way to ask for guidance. If you post your workings and show us where you are stuck, others would be more obliged to help. Peace. __________________ White Group Mathematics Free A Level H2 Maths Resource Site    9th April 2012, 06:43 AM #8 (permalink) Moderator      Posts: 9,462 Join Date: Aug 2008 Likes: 140 Liked 174 Times in 130 Posts Gender: Re: Discriminants and roots problem Tweet know of the formula to solve quadratic equation? x = -b +/- sqrt(b^2-4ac)/2a. also, matching power coefficients? they will help in Q1. __________________ *Have fun in SGClub but pls READ the RULES, Report Bad Posts and Give Reputation to Good Ones!* Last edited by workingtoohard; 9th April 2012 at 06:44 AM.    9th April 2012, 08:42 AM #9 (permalink) Cool SGClubber  Posts: 259 Join Date: Dec 2009 Likes: 10 Liked 7 Times in 6 Posts Gender: Re: Discriminants and roots problem Tweet Originally Posted by whitecorp Posting a long list of questions and their answers is not the way to ask for guidance. If you post your workings and show us where you are stuck, others would be more obliged to help. Peace. Alright, I apologize For Q1, I will try since there is a hint now Here are how I attempt the questions: For Q2, I do not know how to start working For Q3, a)i) 3x^2 + 2kx - k =0 (2k)^2 - 4(3)(-k) = 0 4k^2 - 12(-k) = 0 4k^2 + 12k = 0 4k = 0 or k + 3 = 0 k = 0 (rejected) or k = -3 for ii) 4k(k + 3) > or equal to 0 4k > or equal to 0, k + 3 > or equal to 0 k> or equal to 1/-3 <- is that what they mean by reciprocal? iii) 4k(k + 3) > or equal to 0 4k(k + 3)^2 > or equal to 0 4k > or equal to 0, (k + 3)^2 > or equal to 0 (k^2 + 6k + 9) > or equal to 0 <- from here if I factorise out, it is still the same so I do not know what to do b) 4(x+1)(x-4) = k (4x+4)(x-4) = k 4x^2 - 12x - 16 - k = 0 4x^2 - 12x - 16 - k = 0 (-12)^2 - 4(4)(-16-k) > or equal to 0 - 8 144 + 256 + 16k > or equal to 0 - 8 400 + 16k > or equal to 0 - 8 400 < or equal to -16k - 8 408 < or equal to -16k -25.2 < or equal to K For Q4 2x^2 + 7x + 9 = 0 roots are A + B a = 2, b = 7, c = a A+B = 7/2 AB = a/2 4x^2 + bx + 16 = 0 a = 4, b = b, c = 16 A+B = -b/4 AB = 4 A^2+B^2 = (A+B)^2 - 2AB = (-b/4)^2 - 2(4) = b^2/16 - 81 A^2B^2 = (AB)^2 = (4)^2 = 16 <- from this point, I am not sure what to do next For Q5 3x^2 - squareroot24x - 2 = 0 a = 3, b = -squareroot24, c=-2 m+n = squareroot24/3 mn= -2/3 4/m - 2/n = 4n - 2m/mn = (4n)^2 + (2m)^2 - 2mn/mn = 16n^2 + 4m^2 - 2mn/mn = 4(4n^2 + m^2) - 2mn/mn <- from this point, I do not know how to factorise 4(4n^2 + m^2) into somthing like (m + n) so that I can sub m + n into it    9th April 2012, 09:45 AM #10 (permalink) New SGClubber Posts: 28 Join Date: Oct 2010 Likes: 4 Liked 2 Times in 2 Posts Gender: Re: Discriminants and roots problem Tweet Q1a) Quadratic equations are in the form of ax²+bx+c=0. When the question says that the equation has real roots, it means the discriminant b²-4ac is greater than or equal to zero. 1b.) When quadratic equations have equal real roots, the discriminant b²-4ac=0. From the two given equations you can derive 2 new simultaneous equations involving only p and q through the use of aforementioned statement regarding the discriminant. 2.) You are given the equation of a curve and two points on the curve. First, substitute x=0 into the equation and you find that a=5. Since anything to the power of 0 = 1. Subsequently substitute the values of x=2/3, y=5/4 and a=5. 3ai.) Good job. 3aii.) The reciprocal of x is 1/x. 3aii and 3aiii.) You should use (x-a)(x-1/a)=0 and (x-a)(x-2a)=0 respectively. 3b.) Use (x-a)(x-(a+8))=0. 4.) You have careless mistake. your (A+B) should equal -7/2. 5.) (a-b)²=a²-2ab+b²=a²+b²-2ab=[(a+b)²-2ab]-2ab=(a+b)²-4ab   Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post whitecorp Math Help 0 28th January 2012 09:30 AM *StarDust* Mobile Talk 2 23rd August 2011 02:00 PM babylady Fashion & Beauty 0 6th August 2011 11:40 AM rival2008 SGClub Cafe 9 1st June 2009 09:04 PM Voodoo Vince School Life 1 26th January 2008 06:49 PM Featured Photos by marisoljames322 · · · Member Galleries 20359 photos13619 comments by marisoljames322 · · · Member Galleries 20359 photos13619 comments by pdsubbu · · · Member Galleries 20359 photos13619 comments by Vikas Dhar · · · Photography 35 photos36 comments by aaudreygan · · · Guy Photos 1581 photos946 comments by aaudreygan · · · Girl Photos 4351 photos28606 comments by a8paris · · · Guy Photos 1581 photos946 comments by a8paris · · · Guy Photos 1581 photos946 comments by aaricia · · · Girl Photos 4351 photos28606 comments by aaricia · · · Girl Photos 4351 photos28606 comments Copyright© 2004-2013 SGClub.com. 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