If a=0 and b≠0 in p(x)=ax³+bx²+cx+d, what is the degree of p(x)?
Answer and explanation
Correct answer: 2
The degree of a nonzero polynomial is the greatest exponent of x whose coefficient is nonzero. Since a=0, the cubic term ax³ disappears completely. The next term is bx², and b≠0 guarantees that this term remains present. Therefore the highest surviving power is x², so degree(p)=2 and option C is correct. The value of c or d does not affect the degree once a nonzero x² term is already present. Option D incorrectly retains the vanished cubic term. Option B would be possible only if b were also zero and c were nonzero, while option A would describe a nonzero constant polynomial, not the general expression under the stated condition. The condition b≠0 is essential because it prevents further reduction of the degree.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The degree of a nonzero polynomial is the greatest exponent of x whose coefficient is nonzero. Since a=0, the cubic term ax³ disappears completely. The next term is bx², and b≠0 guarantees that this term remains present. Therefore the highest surviving power is x², so degree(p)=2 and option C is correct. The value of c or d does not affect the degree once a nonzero x² term is already present. Option D incorrectly retains the vanished cubic term. Option B would be possible only if b were also zero and c were nonzero, while option A would describe a nonzero constant polynomial, not the general expression under the stated condition. The condition b≠0 is essential because it prevents further reduction of the degree.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
