Q1
For ax²+bx+c, the sum of zeroes equals:
A-b/a
Bc/a
Cb/a
D-c/a
CBSEClass 10 (CBSE)MathematicsCh 2 · Topic 2
Relationship Between Zeroes and Coefficients
Learning the formulas connecting a polynomial's zeroes to its coefficients.
Core concept
For example, to find a quadratic polynomial whose zeroes sum to 5 and whose product is 6, we can construct it as x² - (sum)x + (product) = x² - 5x + 6. This relationship is derived directly from expanding the factored form of a quadratic, (x-zero1)(x-zero2), and comparing coefficients — a technique that connects the factored, zero-based view of a polynomial to its standard coefficient-based form.
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• For ax²+bx+c: sum of zeroes = -b/a, product of zeroes = c/a.
• A quadratic can be constructed from its zeroes' sum and product: x² - (sum)x + (product).
• This relationship comes from expanding the factored form (x-zero1)(x-zero2).
• It connects the factored (zero-based) view to the standard coefficient-based form of a quadratic.