SS2 First Term Further Mathematics Lesson Note – Roots of Quadratic Equation

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WEEK EIGHT

TOPIC: ROOTS OF QUADRATIC EQUATION 1

SUB-TOPICS:

• Quadratic equation (completing the square and formula method).
• Sum and product of roots of quadratic equation.
• Finding quadratic equation given sum and product of roots, x² – (sum of roots) + (product) = 0.
• Condition for quadratic equation to have: (i) Equal roots (b² = 4ac) (ii) Real roots b² > 4ac (iii) No roots b² < 4ac

SUB-TOPIC 1

Quadratic equation (completing the square and formula method).

A quadratic equation (trinomial) in one variable is a three termed equation in which the highest power of the variable is two. The general quadratic equation in variable x is of the form ax² + bx + c = 0 where a ≠ 0.

In general, a quadratic equation has two solutions which may or may not b+e equal.

There are four major methods of solving quadratic equations. They are:

• factorization method;
• completing the square method;
• formula method;
• graphical method.

Factorisation

Examples

Solve the following by factorization

1. x² -2x – 8=0
2. 15x² + 14x – 8=0

Solution

(a) Product of 1st and 3^rd term = -8x²

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