- Ab
- Bc
- Ca
- DBoth b and c
Step-by-Step Solution
Zeroes α and −α add to 0, and the sum equals , so forces (for example , with zeroes 3 and −3). c cannot be 0 — that would make 0 itself one of the zeroes; and a is never 0 in a quadratic.
Answer: A) b
The two zeroes of a quadratic are equal in magnitude but opposite in sign. Which coefficient must be zero?
Class 10PolynomialsAlgebra — Polynomials
Key idea: Relationship between zeros and coefficients (quadratic)
If α and β are zeros of , then:
**α + β = −/a** (sum of zeros).
**α · β = /a** (product of zeros).
**Why**: − α) − β) = [ − (α+β) + αβ].
Matching coefficients with : coefficient of → −(α+β) = /a → α+β = −/a, and constant: αβ = /a.
**Reverse use**: To form a quadratic with given zeros α, β, write
[ − (α+β) + αβ]
for any non-zero constant (usually ).
**α + β = −/a** (sum of zeros).
**α · β = /a** (product of zeros).
**Why**: − α) − β) = [ − (α+β) + αβ].
Matching coefficients with : coefficient of → −(α+β) = /a → α+β = −/a, and constant: αβ = /a.
**Reverse use**: To form a quadratic with given zeros α, β, write
[ − (α+β) + αβ]
for any non-zero constant (usually ).
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