T Madas Introducing Some Facts Associated with Quadratic

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© T Madas

© T Madas

Introducing Some Facts Associated with (Quadratic) Equations © T Madas

Introducing Some Facts Associated with (Quadratic) Equations © T Madas

Equations Linear Equations Quadratic Equations Cubic Equation Quartic Equation Quintic Equation Irrational Equation Trigonometric

Equations Linear Equations Quadratic Equations Cubic Equation Quartic Equation Quintic Equation Irrational Equation Trigonometric Equation © T Madas

Equations A Quadratic Equation has the unknown (variable) appearing as a square. Quadratic Equations

Equations A Quadratic Equation has the unknown (variable) appearing as a square. Quadratic Equations It may also have the unknown appearing without powers and/or constant numbers but nothing else © T Madas

Equations A Quadratic Equation has the unknown (variable) appearing as a square. Quadratic Equations

Equations A Quadratic Equation has the unknown (variable) appearing as a square. Quadratic Equations The most general form of a quadratic equation is: where a, b and c are constants Do you remember a similar expression from some other topic? © T Madas

Equations We can rearrange these quadratic equations to this form: The most general form

Equations We can rearrange these quadratic equations to this form: The most general form of a quadratic equation is: where a, b and c are constants Do you remember a similar expression from some other topic? © T Madas

Solving Quadratics which Factorise © T Madas

Solving Quadratics which Factorise © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 Either x + 9 = 0 Or x – 1 = 0 2 distinct roots check © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 Either x + 5 = 0 Or x + 2 = 0 2 distinct roots check © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 2 distinct roots © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 2 distinct roots © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 Repeated root © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 2 distinct root © T Madas

To solve a quadratic equation we almost certainly want to have the equation in

To solve a quadratic equation we almost certainly want to have the equation in the form ax 2 + bx + c = 0 2 distinct root © T Madas

Solving Special Quadratics © T Madas

Solving Special Quadratics © T Madas

Solving Special Quadratic Equations When the x term is missing 2 distinct roots Alternative

Solving Special Quadratic Equations When the x term is missing 2 distinct roots Alternative approach 2 distinct roots If you are using this approach be very careful with your answer! © T Madas

Solving Special Quadratic Equations When the x term is missing 2 distinct roots Alternative

Solving Special Quadratic Equations When the x term is missing 2 distinct roots Alternative approach 2 distinct roots © T Madas

Solving Special Quadratic Equations When the x term is missing 2 distinct roots Alternative

Solving Special Quadratic Equations When the x term is missing 2 distinct roots Alternative approach 2 distinct roots © T Madas

Solving Special Quadratic Equations When the number term is missing 2 distinct roots ©

Solving Special Quadratic Equations When the number term is missing 2 distinct roots © T Madas

Solving Special Quadratic Equations When the number term is missing 2 distinct roots ©

Solving Special Quadratic Equations When the number term is missing 2 distinct roots © T Madas

More Examples © T Madas

More Examples © T Madas

Quadratic equations which require some initial manipulations Solve the equation: © T Madas

Quadratic equations which require some initial manipulations Solve the equation: © T Madas

Quadratic equations which require some initial manipulations Solve the equation: © T Madas

Quadratic equations which require some initial manipulations Solve the equation: © T Madas

© T Madas

© T Madas