Relationship between zeros and coefficients of a quadratic polynomial
If α and β are the zeros of the quadratic polynomial ax^2+bx+c, then α+β=-b/a and αβ=c/a, where a is not zero.
Practice This ConceptMain explanation
Teacher explanation
This relationship is one of the most useful results in Class 10 polynomials. It helps us find the sum and product of zeros without factorising every time. It also helps in constructing polynomials and checking answers quickly. Students should remember that the coefficient signs matter carefully.
Example
For 2x^2-7x+3, the sum of zeros is 7/2 and the product of zeros is 3/2.
Simple analogy
Sum gets the minus sign; product does not.
Common confusion
Students often forget the minus sign in the sum formula or write product as -c/a. The product is c/a, not negative c/a.
Exam tip
For ax^2+bx+c, always write sum as -b/a and product as c/a before substituting numbers.
Answer writing and exam use
1-mark use
Write the exact meaning of relationship between zeros and coefficients of a quadratic polynomial in one clean line.
2-mark use
Define relationship between zeros and coefficients of a quadratic polynomial and add one example or condition.
3-mark use
Explain relationship between zeros and coefficients of a quadratic polynomial, 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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