Everything Maths Grade 11

Solving Quadratic Equations 7 8.1 Introduction EMBAF In Grade 10, the basicsof solving linear equations, quadratic equations, ex ...

7.2 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS We see that sv =− 12 and s + 2v =− 5. This is a set of simultaneous equations in s and ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.2 a^2 − 3 a− 10 = 0 Step 2 : Factorise the trinomial (a + 2)(a− 5) = 0 Step 3 : Solve th ...

7.2 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS (2b + 3)(b− 1) = 0 2 b + 3 = 0 or b− 1 = 0 b = − 3 2 or b = 1 Step 5 : Check solutions ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.3 7.3 Solution by Completing the Square EMBAH We have seen that expressions of the form: ...

7.3 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS Write the left hand side as a perfect square: (x + 1)^2 − 4 = 0 You should then be ab ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.3 (x + 1)(x− 11) = 0 ∴ x =−1 or x = 11 Example 5: Solving Quadratic Equations by Complet ...

7.4 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS Leave the left hand sidewritten as a perfect square (x− 2)^2 = 12 Step 9 : Take the sq ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.4 Consider the general form of the quadratic function: f(x) = ax^2 + bx + c. Factor out ...

7.4 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS Example 6: Using the quadratic formula QUESTION Find the roots of the function f(x) = ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.4 SOLUTION Step 1 : Determine whether theequation can be factorised The expression canno ...

7.4 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 9 t^2 − 7 t− 9 = 0 2 t^2 + 3t + 2 = 0 t^2 + t + 1 = 0 More practice video solutions ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.5 7.5 Finding an Equation When You Know its Roots EMBAJ We have mentioned before that th ...

7.5 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS Step 1 : Product of two brackets Notice that if x =−^32 then 2 x + 3 = 0 Therefore the ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.5 Δ Δ < 0 : imaginary roots Δ≥ 0 : real roots Δ = 0 equal roots Δ > 0 unequal root ...

7.5 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS [IEB, Nov. 2004, HG] Consider the equation: k = x^2 − 4 2 x− 5 where x�=^52 (a) Find ...

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.5 (a) Use this formula to solve the equation: 2 x^2 + x− 3 = 0 (b) Solve the equation ag ...

Solving Quadratic Inequalities 8 9.1 Introduction EMBAM Now that you know howto solve quadratic equations, you are ready to move ...

CHAPTER 8. SOLVINGQUADRATIC INEQUALITIES 8.2 (2x− 1)^2 ≤ 0 Step 3 : Solve the equation f(x) = 0 only when x =^12. Step 4 : Write ...

8.2 CHAPTER 8. SOLVINGQUADRATIC INEQUALITIES f(x) sign of f(x) Region A x < 2 f(1) = 2 + Region B x = 2 f(2) = 0 + Region C 2 ...