QUADRATIC EQUATIONS [ FOR UK C1 SYLLABUS & CBSE ]

QUADRATIC EQUATIONSExercise 1Solving Quadratic Equations By Factorisation(i) Solve : x2 – x – 12 = 0(ii) 2x2 – 5x + 3 = 0(iii) 6x2 – x – 2 = 0 (iv) Find the roots of:2x2 + x – 6 = 0(v) Find the roots of 100 x2 – 20 x + 1 = 0(vi) 3x2 - 2 + 2 = 0Solving equations by completing squaresExercise 2(1) Solve : ( x – 5 )2 = 9(2) (2x + 7)2 = 1(3) Using the method of “ completing square”, find the roots of X2 + 4x – 5 = 0(4) x2 – 8x = 65(5) x2 + 10 x = 264(6) Using the method of “completing square”, solve : 3x2 – 5x + 2 = 0(7) Solve 2x2 – 5x + 3 = 0 by the method of completing square(8) Find the roots of the equation 5x2 – 6x – 2 = 0 by the method of completing the square.QUADRATIC FORMULA Given ax2 + bx + c = 0. Prove that Exercise 3Using Quadratic formula solve the following equations(1) 3x2 – 5x + 2 = 0(ii) x2 + 2x - 143 = 0(iii) 2x2 + x – 528 = 0(iv) (v) x2 + 4x + 5 = 0 (vi) (vii) x2 + x + 1 = 0(viii) NATURE OF ROOTSExercise 4(i) Find the discriminant of the quadratic equation 2x2 – 4x + 3 = 0 and hence find the nature of its roots(2) Find the nature of the roots of 3x2 – 2x + 1/3 = 0. Find these roots if they are real.(3) Find the value of k if the equation 2x2 + k x + 3 = 0 has real roots(4) Find the value of k for which the following quadratic equation has two equal roots kx (x - 2 ) + 6 = 0NATURE OF ROOTSWhen the value of b2 – 4ac < 0 ( or negative ), the equation will have no real roots.When the value of b2 – 4ac = 0 , the equation will have equal roots .When the value of b2 – 4ac > 0 ( or positive ), the equation will have two different real roots.(ix) PAST C1 EXAM QUESTION 2007 June(x) 2008 January ( C2 Exam question /Edexcel )2008 June ( past Exam question)(xi)Exercise 5Qn . Sketch the graphs of the following quadratic functions (i) y = x2 – 4(ii) y = -x2 + 9(iii) y = x2 – 2x - 8(iv) y = 10 + 3x – x2(v) y = x2 – 3x – 4(vi) y = -x2 + 3x +4(vii) y = x2 – 4x + 4(viii) y = - 1 + 2x - x2(ix) y = x2 + 2x + 2(x) y = -x2 + 2x – 5ANYONE NEEDS TUITION IN THIS TOPIC CAN CONTACT ME AT:georgeignatiusxx@gmail.com [ google talk]georgeignatius9 [Skype ]