For which value of \(a\) will the polynomial \(p(x)=(a-2)x^3+4x^2+1\) have degree 2?
Answer and explanation
Correct answer: \(a=2\)
For the polynomial to have degree 2, the coefficient of \(x^3\) must be zero so that the cubic term disappears and \(4x^2\) becomes the highest-degree term. Thus, \(a-2=0\), giving \(a=2\). For example, if \(a=4\), the coefficient of \(x^3\) is 2, so the degree remains 3. Exam tip: To reduce a polynomial’s degree, set the coefficient of its highest-power term equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(a=2\)
Why is this the correct answer?
For the polynomial to have degree 2, the coefficient of \(x^3\) must be zero so that the cubic term disappears and \(4x^2\) becomes the highest-degree term. Thus, \(a-2=0\), giving \(a=2\). For example, if \(a=4\), the coefficient of \(x^3\) is 2, so the degree remains 3. Exam tip: To reduce a polynomial’s degree, set the coefficient of its highest-power term equal to zero.
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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