- A
- B
- C
- DAny non-zero value of a
Step-by-Step Solution
A quadratic polynomial has degree exactly 2, so the term must disappear: leaves . Any non-zero a keeps the highest power at 3, so the polynomial stays cubic.
Answer: A)
For what value of a is a quadratic polynomial?
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 ).
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Polynomials practice questions
More Class 10 Polynomials practice
For p(x) = x³ − 4x² + 3x − 7, the value of p(−2) is ____.Anita checks whether x = 3 is a zero of p(x) = 2x² − 5x − 3 by evaluating p(3). What…The zero of a linear polynomial ax + b is -b/a. Use this rule to find the zero of 5x − 2.A shop’s stock of notebooks t days after a school order begins is given by N(t) = 240 −…The graph of y = p(x) is a parabola that touches the x-axis at exactly one point without…