Quadratic polynomial and its zeros
A quadratic polynomial is a polynomial of degree 2, usually written as ax^2+bx+c where a is not zero. Its zeros are the values of x that make the polynomial equal to 0.
Practice This ConceptMain explanation
Teacher explanation
A quadratic polynomial can have either two real zeros, one repeated zero, or no real zero, depending on the graph and the discriminant in later chapters. In Class 10 polynomials, the main idea is to find the values of x that satisfy ax^2+bx+c=0 and to connect those values with the graph.
Example
For x^2-5x+6, the zeros are 2 and 3 because (x-2)(x-3)=0.
Simple analogy
Quadratic means up to two zeros.
Common confusion
Students sometimes think a quadratic must always have two different zeros. Repeated roots are also possible.
Exam tip
If a quadratic factorises neatly, first break it into factors and then set each factor equal to zero.
Study the quadratic polynomial and its zeros diagram carefully
Use the labelled diagram to keep quadratic polynomial and its zeros clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of quadratic polynomial and its zeros in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on quadratic polynomial and its zeros.
Revision cue
Revise quadratic polynomial and its zeros through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of quadratic polynomial and its zeros in one clean line.
2-mark use
Define quadratic polynomial and its zeros and add one example or condition.
3-mark use
Explain quadratic polynomial and its zeros, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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