Quartic equations Study guides, Revision notes & Summaries

MATH 3326 Quiz for Final Exam Review, History of Mathematics: Covers chapters 1-6 Nicole Oresme (1320-1382) Elementary proof of divergence of harmonic series. Nicolo Tartaglia (1499-1557) Formula for solving cubic equations. Gerolamo Cardano (1501-1576) Publishing formulas for solving cubic and quartic equations which were done by other mathematicians. Francois Viète (1540-1603) Formula connecting the roots and coefficients of polynomials John Napier (1550-1617) Invention of logarit...

MATH 3326 Quiz for Final Exam Review, History of Mathematics: Covers chapters 1-6 Nicole Oresme () Elementary proof of divergence of harmonic series. Nicolo Tartaglia () Formula for solving cubic equations. Gerolamo Cardano () Publishing formulas for solving cubic and quartic equations which were done by other mathematicians. Francois Viète () Formula connecting the roots and coefficients of polynomials John Napier () Invention of logarithms Bonaventura Cavalieri () A principle to...

MATH 3326 Quiz for Final Exam Review, History of Mathematics: Covers chapters 1-6 Nicole Oresme () Elementary proof of divergence of harmonic series. Nicolo Tartaglia () Formula for solving cubic equations. Gerolamo Cardano () Publishing formulas for solving cubic and quartic equations which were done by other mathematicians. Francois Viète () Formula connecting the roots and coefficients of polynomials John Napier () Invention of logarithms Bonaventura Cavalieri () A principle to...

1 The roots of the equation 4x 4 -2x 3 -3x+2 = 0 are a, b, c and d. By using a suitable substitution, find a quartic equation whose roots are a+2, b+2, c+2 and d+2 giving your answer in the form at4 + bt3 + ct2 + dt + e = 0, where a, b, c, d, and e are integers. [5] 2 The lines L1 and L2 have the following equations. J-5N J 5 N L : r = K 6 O + m K O 1 K O K-2O L 15P K -2 O J24N J 3 N L : r = K 1 O +n K 1 O 2 K O K O L -5P L -4P (a) Show that L1 and L2 inte...

Pure Maths A Level Questions and Answers 100% Pass Gradient y2-y1/x2-x1 Length of a line sqrt((x2-x1)^2+(y2-y1)^2) Midpoint (x1+x2/2, y1+y2/2) How do you know if two lines are perpendicular? When you multiply the gradients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras to show there is a right angle How do you know if two lines are parallel? The gradients should be the same What should you always remember when finding the square roots? T...

1. Gradient y2-y1/x2-x1 2. Length of a line sqrt((x2-x1)^2+(y2-y1)^2) 3. Midpoint (x1+x2/2, y1+y2/2) 4. How do you know if two lines are perpendic- ular? When you multiply the gra- dients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras to show there is a right angle 5. How do you know if two lines are parallel? The gradients should be the same 6. What should you always remember when finding the square roots? The answer cou...

Exam (elaborations) TEST BANK FOR Calculus 8th Editon (3 Volume Set) By Ron Larson, Robert P. Hostetler and Bruce H. Edwards (Study And Solutions Guide) C H A P T E R P Preparation for Calculus Section P.1 Graphs and Models . . . . . . . . . . . . . . . . . . . . . . 2 Section P.2 Linear Models and Rates of Change . . . . . . . . . . . . . 7 Section P.3 Functions and Their Graphs . . . . . . . . . . . . . . . . . 14 Section P.4 Fitting Models to Data . . . . . . . . . . . . . . . . . . . ...

SMA 2101: CALCULUS I ⃝c Francis O. Ochieng Department of Pure and Applied Mathematics Jomo Kenyatta University of Agriculture and Technology Course content • Functions: definition, domain, range, codomain, composition (or composite), inverse. • Limits, continuity and differentiability of a function. • Differentiation by first principle and by rule for x n (integral and fractional n). • Other techniques of differentiation, i.e., sums, products, quotients, chain rule; their a...

Maths A level Questions and Answers Rated A What is 2^x multiplied by 3^x? Let x=2 2^2 X 3^2 = 4 X 9 = 36 36=6^2 So answer is 6^x How would you solve (x^3 - 2x)/3x^2 Break down fraction to (x^3/ 3x^2) - (2x/3x^2) then continue to simplify fractions and cancel out like terms How would you factorise 4x^4 - 13x^2 + 9 Change 4x^4 and 13x^2 into 4(x^2)^2 and 13(x^2) Then let (x^2) be y and substitute y to get 4y^2-13y+9=0 which factorises into (4y-9)(y-1)=0 Which is equal to (4x^2 -9)(x^2 -1) This ...

1. Order of a matrix Number of rows by number of columns 2. Square matrix Matrix of order NxN 3. Leading diagonal Diagonal of matrix from top left to bottom right 4. Conditions for two matrices to be equal - must have same order - each element in one matrix must be equal to the corresponding ele- ment in the other 5. Matrices which you can't add are... non-conformable for addition 6. Matrices which you can't multiply are... non-conformable for multiplication 7. Matrix...