# maths genie a level the discriminant

Tes Global Ltd is registered in England (Company No 02017289) with its registered office … Edexcel A Level Pure Maths exam revision with questions and model answers for Using the Discriminant 1. This website and its content is subject to our Terms and Conditions. Using the discriminant with circles 1 November 14, 2018 Aug 21­5:12 PM L.O. New AS and A Level Content 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. • Answer all questions and ensure that your answers to … Back to Top. with Mince Pies. 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 AS/A Level Mathematics The Discriminant Instructions • Use black ink or ball-point pen. 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. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). b² – 4ac = 0 Roots are real and equal. If the quadratic has one real root, then $${b^2} - 4ac = 0$$. All A level questions arranged by topic. The discriminant for a quadratic equation $$a{x^2} + bx + c = 0$$ is $${b^2} - 4ac$$. The nature and co-ordinates of roots can be determined using the discriminant and solving polynomials as part of Bitesize Higher Maths 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 \ (a {x^2} + bx + c = 0\) is \ ({b^2} - 4ac\). Find your group chat here >> start new discussion reply. . 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 ). What type of roots the equation has can be shown by the discriminant. And the types of root the equation has can be worked out as follows: Find the nature of the roots of $$2{x^2} + 3x - 6 = 0$$. Example x 2 - 5x + 2 = 0. a = 1, b = -5, c = 2 Welcome to A-Level Maths. Pearson Education accepts no responsibility whatsoever for the accuracy or method of working in the answers given. Maths Genie - A Level Exam Papers - Exam Papers, Mark Schemes and Solutions A Level Exam Papers (Edexcel) A Level exam papers and mark schemes. 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). x x 6M —10 ID —- / O / rv-7 net 76 — / 00 / rvv —S+ãj Since $${b^2} - 4ac\textgreater0$$, the roots are real and unequal. Maths Genie keyboard_arrow_up. Formula Book New AS and A Level Content Edexcel AS and A Level Data Set. This website and its content is subject to our Terms and Conditions. If the quadratic has two distinct roots, the discriminant must be positive, i.e. Formula Book This page is for the new AS and A Level Maths specification for first teaching September 2017. Show that the particle is never at rest. Tes Global Ltd is registered in England (Company No 02017289) with its registered office … . 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. The discriminant is given by where a=p, b=3p and c=-5. All A level questions arranged by topic. lhh2003 ... As level maths - functions and alegbra inequalities help … Find the possible values of k. [2] [3] The quadratic equation x2 + kx + k = O has no real roots for x. A Level (Edexcel) This page is for the new AS and A Level Maths specification for first … 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”. Discriminant is NOT given in the Higher Maths exam – please memorise. . In GCE 'O' Level A-Math, there is a commonly asked question in Quadratic Equations. 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. 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 $$x$$. Made by expert teachers. “2 roots” is not accepted. Back to Top. Exam questions for C1, C2, C3, C4, S1 and M1 arranged by module and topic. 1 —6 8 rvt0C — / Ina C 100 —72 g¼+ll+ — GSC a 100 1 . The Previous A Level Specification Page By using discriminant considerations, show that the above quadratic equation will always have real solutions. 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. b² – 4ac > 0 Roots are real and distinct. The Discriminant. b² – 4ac < 0 No real roots. GCSE Revision Cards. Find the value(s) of $$k$$ if $${x^2} + 2kx + 36 = 0$$ has one real root. Therefore we have to solve this using $$a = 1,\,b = 2k\,and\,c = 36$$, ${(2k)^2} - (4 \times 1 \times 36) = 0$. determine the nature of the roots and then solve. Maths Genie face reveal? Announcements Government announces GCSE and A-level students will receive teacher awarded grades this year >> Applying to uni? For 2 real equal roots, it is equal to 0. The discriminant is \ ({b^2} - 4ac\), which comes from the quadratic formula and we can use this to find the nature of the roots. Pearson Education accepts no responsibility whatsoever for the accuracy or method of working in the answers given. 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. 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. Watch. (i) Find the discriminant of kx2 — 4x + k in terms of k. (ii) The quadratic equation kx2 — 4x + k = O has equal roots. 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. Discriminant A-level; Videos; discriminant; Post navigation. For the quadratic function $$y = (2x + 3)(x - 5)$$ determine the nature of the roots and then solve. In general, we could apply the formula to work out the solutions of a quadratic function ax 2 +bx+c=0.. Firstly we need to remove the brackets using FOIL: Using the discriminant to find the nature: $= {( - 7)^2} - (4 \times 2 \times - 15)$. Maths revision video and notes on the topics of quadratic equations and the discriminant. Roots and discriminant of a quadratic equation In video I explain what we mean by roots and the discriminant of a quadratic equation. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; October 10, 2013 corbettmaths. A video revising the techniques and strategies for working with the factor theorem (GCSE Further Maths & A-Level Only). For the new A Level I am using the Casio fx-991EX Classwiz Calculator: These videos are made by Maths Genie. For the new A Level I am using the Casio Classwiz Calculator: CASIO FX … Here I introduce this playlist for the most up to date 2017 spec, covering all exam boards AQA, Edexcel, OCR and OCR MEI. 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 … GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. $$= 169\textgreater0$$ therefore roots are real and unequal. Wasn't entirel Our tips from experts and exam survivors will help you through. Consider the three possible combinations: The points where the graph cuts the x … Maths Genie - A Level Maths revision page. This page is for the new AS and A Level Maths specification for first teaching September 2017. The Quadratic Formula Hegarty keyboard_arrow_up. Source: N5 Maths, Specimen, P2, Q12. Show that C and L, intersect for all values of c. SYN-A , … 0. reply. The discriminant for a quadratic equation. Read about our approach to external linking. 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? or . 1)View SolutionHelpful TutorialsSubstitution method for linear and non-linear equationsRoots and […] The wording is important. For no real roots, it is less than 0. These videos are made by the award winning Hegarty Maths. Previous Pi…. Be sure to visit his website for top-quality GCSE and A Level revision resources. 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. Many students fell into the trap set up by teachers and examiners. The nature and co-ordinates of roots can be determined using the discriminant and solving polynomials. • Fill in the boxes at the top of this page with your name. Page 1 of 1 ... A level maths Maths study tips. The discriminant is for a quadratic in the form For two distinct real roots, it must be strictly greater than 0. 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. Next Indices exam questions. It follows that it is then given by . 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