If (p(x)=ax^2+bx+c) and (a\neq0), what type of polynomial is (p(x))?
Answer and explanation
Correct answer: Quadratic
The degree of a polynomial is the greatest exponent of the variable whose coefficient is not zero. In \\(p(x)=ax^2+bx+c\\), the coefficient of \\(x^2\\) is a, and the question states that \\(a\\ne0\\). Therefore the quadratic term is genuinely present, so the degree is 2. A polynomial of degree 2 is called a quadratic polynomial, making option B correct.
The values of b and c may be zero or nonzero, but they cannot remove the nonzero \\(ax^2\\) term. Hence the expression cannot become linear, constant, or cubic. The condition \\(a\\ne0\\) is essential: if a were zero, the degree could fall depending on b and c. Here that condition fixes the highest nonzero power as 2.
Frequently asked questions
What is the correct answer to this question?
Quadratic
Why is this the correct answer?
The degree of a polynomial is the greatest exponent of the variable whose coefficient is not zero. In \\(p(x)=ax^2+bx+c\\), the coefficient of \\(x^2\\) is a, and the question states that \\(a\\ne0\\). Therefore the quadratic term is genuinely present, so the degree is 2. A polynomial of degree 2 is called a quadratic polynomial, making option B correct.
The values of b and c may be zero or nonzero, but they cannot remove the nonzero \\(ax^2\\) term. Hence the expression cannot become linear, constant, or cubic. The condition \\(a\\ne0\\) is essential: if a were zero, the degree could fall depending on b and c. Here that condition fixes the highest nonzero power as 2.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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