Secondary 3 G2 Mathematics Tutor Bukit Timah | Quadratic Discriminant and Number of Roots. Did you know? A quadratic can have two, one or no real roots.
This guide helps Secondary 3 G2 Mathematics students in Bukit Timah understand quadratic discriminant and number of roots through concise explanations, worked examples and checks. For ax²+bx+c=0 with a nonzero, the discriminant is D=b²−4ac. It determines how many distinct real solutions exist.
Quick answer: Quadratic Discriminant and Number of Roots
A quadratic can have two, one or no real roots. For ax²+bx+c=0 with a nonzero, the discriminant is D=b²−4ac. It determines how many distinct real solutions exist.
Worked example: the first important method
For x²−5x+6=0, D=25−24=1, so there are two distinct real roots, 2 and 3.
Worked example: change the conditions
For x²−4x+4=0, D=16−16=0, so the root 2 is repeated. The parabola touches the x-axis once.
How to check the result
For x²+x+1=0, D=1−4=−3, so there are no real roots. Its graph does not meet the x-axis. Always identify a, b and c including their signs. The discriminant is a useful extension when comparing quadratic graphs and solving equations.
A practical revision plan
First, identify the given information and define the unknown. Next, solve a worked example with every reason or algebraic step shown. Then change the numbers or diagram and attempt the question independently. Finally, revisit it after several days. Always identify a, b and c including their signs. The discriminant is a useful extension when comparing quadratic graphs and solving equations.
Frequently asked questions
What should I check first? Read the question, identify the given quantities and the required result. Why can the answer look plausible but be wrong? A misplaced sign, incorrect diagram correspondence or wrong unit can invalidate an otherwise neat calculation. How can parents help? Ask the learner to explain the first step, not simply quote a formula.
Official syllabus and learning support
Use the 2027 SEC G2 Mathematics K210 syllabus for the precise assessment scope. The unchanged eduKateSG small-group Mathematics reference describes the existing teaching model near Sixth Avenue. Confirm actual Secondary 3 G2 class availability, tutor, timetable and fees directly.
Continue learning
For related Mathematics work, see the right-triangle checking guide, the probability rules guide, and the circle chords and tangents guide.
Ask the student to complete a changed question without prompts and explain why the method works. Always identify a, b and c including their signs. The discriminant is a useful extension when comparing quadratic graphs and solving equations.