# maths genie a level the discriminant

5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. By using discriminant considerations, show that the above quadratic equation will always have real solutions. To be able to apply the discriminant to circles 14/11/18 You know from when we looked at the discriminant that a straight line can either . with Mince Pies. Roots and discriminant of a quadratic equation In video I explain what we mean by roots and the discriminant of a quadratic equation. If the quadratic has one real root, then $${b^2} - 4ac = 0$$. An SQA N5 Maths exam question on the Discriminant is: “Find the range of values of p such that the equation px² – 2x + 3 = 0, p ≠ 0, has no real roots”. Show that C and L, intersect for all values of c. SYN-A , … b² – 4ac > 0 Roots are real and distinct. • Answer all questions and ensure that your answers to … It follows that it is then given by . • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). “2 roots” is not accepted. For the quadratic function $$y = (2x + 3)(x - 5)$$ determine the nature of the roots and then solve. What type of roots the equation has can be shown by the discriminant. and since the question already gave us the quadratic in its factorised form, we will use this to solve to find values for, Dividing and factorising polynomial expressions, Solving logarithmic and exponential equations, Identifying and sketching related functions, Determining composite and inverse functions, Religious, moral and philosophical studies. Example x 2 - 5x + 2 = 0. a = 1, b = -5, c = 2 Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team. b² – 4ac < 0 No real roots. Maths Genie - A Level Exam Papers - Exam Papers, Mark Schemes and Solutions A Level Exam Papers (Edexcel) A Level exam papers and mark schemes. Trinomial coefficients a, b & c (from ax² + bx + c) are substituted into b² – 4ac. A video revising the techniques and strategies for working with the factor theorem (GCSE Further Maths & A-Level Only). Exam questions for C1, C2, C3, C4, S1 and M1 arranged by module and topic. Find the value(s) of $$k$$ if $${x^2} + 2kx + 36 = 0$$ has one real root. This page is for the new AS and A Level Maths specification for first teaching September 2017. Discriminant A-level; Videos; discriminant; Post navigation. To solve the quadratic equation, we make $$y = 0$$ and since the question already gave us the quadratic in its factorised form, we will use this to solve to find values for $$x$$. And the types of root the equation has can be worked out as follows: Find the nature of the roots of $$2{x^2} + 3x - 6 = 0$$. Maths revision video and notes on the topics of quadratic equations and the discriminant. For the new A Level I am using the Casio Classwiz Calculator: CASIO FX … This website and its content is subject to our Terms and Conditions. Maths Genie - A Level Maths revision page. Formula Book New AS and A Level Content Edexcel AS and A Level Data Set. In order for this inequality to hold we must have or (you can see this by sketching and seeing where it is positive – see Inequalities ). And since we are told in question that k is a real number the discriminant is positive and if the discriminant is greater than 0, then there are 2 different real roots, thus answering the question. (i) Writedown the discriminant of x 2 + kx+k in terms of … SYN-Q , proof Question 28 (****) The curve C and the straight line L have respective equations 2 2 1 2 y x − = and y x c= + , where c is a constant. Watch. lhh2003 ... As level maths - functions and alegbra inequalities help … The discriminant is given by where a=p, b=3p and c=-5. Tes Global Ltd is registered in England (Company No 02017289) with its registered office … or . $$= 169\textgreater0$$ therefore roots are real and unequal. Pearson Education accepts no responsibility whatsoever for the accuracy or method of working in the answers given. The b 2-4ac part is called the discriminant and the value of a discriminant could allow us to know the number of real roots that a quadratic function has.In other words, how many times does a quadratic curve cross the horizontal x axis in a graph? These videos are made by the award winning Hegarty Maths. Read about our approach to external linking. The wording is important. The discriminant is for a quadratic in the form For two distinct real roots, it must be strictly greater than 0. For no real roots, it is less than 0. The Previous A Level Specification Page In general, we could apply the formula to work out the solutions of a quadratic function ax 2 +bx+c=0.. All A level questions arranged by topic. This website and its content is subject to our Terms and Conditions. The Quadratic Formula Hegarty keyboard_arrow_up. Therefore we have to solve this using $$a = 1,\,b = 2k\,and\,c = 36$$, ${(2k)^2} - (4 \times 1 \times 36) = 0$. . Using the discriminant with circles 1 November 14, 2018 Aug 21­5:12 PM L.O. The velocity of a particle P at time t seconds is given by v=t^2-14t+50 where t is greater than 0. The discriminant for a quadratic equation. Be sure to visit his website for top-quality GCSE and A Level revision resources. Back to Top. determine the nature of the roots and then solve. 1 —6 8 rvt0C — / Ina C 100 —72 g¼+ll+ — GSC a 100 1 . Page 1 of 1 ... A level maths Maths study tips. A Level (Edexcel) This page is for the new AS and A Level Maths specification for first … GCSE Revision Cards. Source: N5 Maths, Specimen, P2, Q12. This video is part of the Algebra module in GCSE Further Maths & A-Level maths, see my other videos below to continue with the series. The discriminant for a quadratic equation $$a{x^2} + bx + c = 0$$ is $${b^2} - 4ac$$. Edexcel A Level Pure Maths exam revision with questions and model answers for Using the Discriminant 1. • Fill in the boxes at the top of this page with your name. x x 6M —10 ID —- / O / rv-7 net 76 — / 00 / rvv —S+ãj Firstly we need to remove the brackets using FOIL: Using the discriminant to find the nature: $= {( - 7)^2} - (4 \times 2 \times - 15)$. . All A level questions arranged by topic. Pearson Education accepts no responsibility whatsoever for the accuracy or method of working in the answers given. b² – 4ac = 0 Roots are real and equal. The discriminant, D = b 2 - 4ac Note: This is the expression inside the square root of the quadratic formula There are three cases for the discriminant; Case 1: b 2 - 4ac > 0 If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. Made by expert teachers. Announcements Government announces GCSE and A-level students will receive teacher awarded grades this year >> Applying to uni? Back to Top. The nature and co-ordinates of roots can be determined using the discriminant and solving polynomials as part of Bitesize Higher Maths Our tips from experts and exam survivors will help you through. Tes Global Ltd is registered in England (Company No 02017289) with its registered office … Formula Book How the discriminant tells us how many roots a quadratic equation has and the relationship of a quadratic graph to the number of roots based on how it cuts the x-axis. Next Indices exam questions. Discriminant is k2 —4k For no real roots, k2 —4k < O Hence k(k — 4) < O So O < k < 4 Ml 2 Ml Ml 4 For attempted use of the discriminant For correct expression (in any form) For stating their A < O For factorising attempt (or other soln method) For both correct … Previous Pi…. Show that the particle is never at rest. Many students fell into the trap set up by teachers and examiners. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; October 10, 2013 corbettmaths. Welcome to A-Level Maths. Maths Genie keyboard_arrow_up. CASIO FX-991EX Advanced Scientific Calculator, CASIO FX-991EX Advanced Scientific Calculator, The Factor Theorem and Algebraic Division, Quadratics Inequalities and Simultaneous Equations, Sine Rule, Cosine Rule, Area of Any Triangle, Using the Normal Distribution to approximate the Binomial, Mean of Normal Distribution Hypothesis Testing, Probability and Statistical Distributions, Statistical Sampling and Hypothesis Testing. These videos are made by Maths Genie. Here I introduce this playlist for the most up to date 2017 spec, covering all exam boards AQA, Edexcel, OCR and OCR MEI. The Discriminant. A video revising the techniques and strategies for working with the factor theorem (GCSE Further Maths & A-Level Only). Discriminant is NOT given in the Higher Maths exam – please memorise. The discriminant for a quadratic equation \ (a {x^2} + bx + c = 0\) is \ ({b^2} - 4ac\). Edexcel AS and A Level Data Set The discriminant is \ ({b^2} - 4ac\), which comes from the quadratic formula and we can use this to find the nature of the roots. Maths Genie face reveal? For 2 real equal roots, it is equal to 0. 0. reply. If the quadratic has two distinct roots, the discriminant must be positive, i.e. And the types of root the equation has can be worked out as follows: , the roots are real and unequal (diagram A), , the roots are real and equal (diagram B). Since $${b^2} - 4ac\textgreater0$$, the roots are real and unequal. This page is for the new AS and A Level Maths specification for first teaching September 2017. In GCE 'O' Level A-Math, there is a commonly asked question in Quadratic Equations. 1)View SolutionHelpful TutorialsSubstitution method for linear and non-linear equationsRoots and […] New AS and A Level Content The nature and co-ordinates of roots can be determined using the discriminant and solving polynomials. For the new A Level I am using the Casio fx-991EX Classwiz Calculator: (i) Find the discriminant of kx2 — 4x + k in terms of k. (ii) The quadratic equation kx2 — 4x + k = O has equal roots. Roots can occur in a parabola in 3 different ways as shown in the diagram below: In diagram A, we can see that this parabola has 2 roots, diagram B has 1 root and diagram C has no roots. Find your group chat here >> start new discussion reply. Consider the three possible combinations: The points where the graph cuts the x … M1 arranged by module and topic up by teachers and examiners is used for diagrams/sketches/graphs it must be,. 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