Forming quadratic polynomial from given zeros
If α and β are the zeros of a quadratic polynomial, then the polynomial can be written as k(x-α)(x-β), where k is a non-zero constant.
Practice This ConceptMain explanation
Teacher explanation
To form a quadratic polynomial from its zeros, first write the factors x-α and x-β. Then multiply them and, if needed, adjust the leading coefficient using the given information. This is a standard exam skill and often appears as a short construction question.
Example
If the zeros are 2 and 3, one quadratic polynomial is (x-2)(x-3)=x^2-5x+6.
Simple analogy
Zeros change sign inside factors.
Common confusion
Students sometimes write (x+α)(x+β) even when the zeros are positive numbers. The sign inside each factor must be opposite to the zero.
Exam tip
From zeros α and β, use x-α and x-β, then expand carefully.
Answer writing and exam use
1-mark use
Write the exact meaning of forming quadratic polynomial from given zeros in one clean line.
2-mark use
Define forming quadratic polynomial from given zeros and add one example or condition.
3-mark use
Explain forming quadratic polynomial from given zeros, show the method or example, and mention the common mistake.
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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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