Quadratic Functions and Equations in One Variable · 1.1.8
Solving quadratic equation problems
This standard asks students to turn a real-world situation, areas, consecutive numbers, speed, dimensions, into a quadratic equation, solve it by factorisation, completing the square or the formula, then choose the answer that actually fits the situation, rejecting roots that are negative or otherwise physically impossible.
The official learning standard (1.1.8)
“Solve problems involving quadratic equations.”
What it means
This standard asks students to turn a real-world situation, areas, consecutive numbers, speed, dimensions, into a quadratic equation, solve it by factorisation, completing the square or the formula, then choose the answer that actually fits the situation, rejecting roots that are negative or otherwise physically impossible.
How it is examined
In Paper 1, a short item may ask students to form the quadratic equation from a brief word statement or pick the correct pair of roots. In Paper 2, a longer subjective question typically gives a real-life context (area, consecutive integers, motion) and requires forming the equation, solving it, and stating a valid answer with correct units.
Worked example
The length of a rectangular garden is 3 m more than its width. Given that the area of the garden is 108 m², find the width of the garden.
- Let the width be x m, so the length = (x + 3) m.
- Form the equation from the area: x(x + 3) = 108.
- Expand and simplify: x² + 3x − 108 = 0.
- Factorise: (x − 9)(x + 12) = 0.
- Solve: x = 9 or x = −12.
- Reject x = −12 since width cannot be negative.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I know which variable to let as x?
Let x represent the quantity you know least about or the one the question asks for directly, often the smaller value in a comparison, like width when length is given as 'more than' the width. This makes forming the equation from the given relationship straightforward.
What if both roots are positive, how do I choose?
Re-read the question for extra restrictions such as 'the smaller number' or a size limit. If both roots satisfy the situation, some problems accept both as valid answers, so check whether the question asks for one value or all possible values before deciding.
Do I always need to reject a root?
No, only reject a root when it contradicts the physical meaning of the problem, such as a negative length, a fractional number of people, or a value outside a stated range. If both roots are sensible, state both as the answer.