For which value will the degree of ((a+7)x^6-4x^2+9) be (2)?
Answer and explanation
Correct answer: \(a=-7\)
For the polynomial to have degree 2, the coefficient of \(x^6\) must be zero. Thus, \(a+7=0\), which gives \(a=-7\). For this value, the polynomial becomes \(-4x^2+9\), whose degree is 2. If \(a=0\), the coefficient of \(x^6\) is still 7, so the degree remains 6. Exam tip: First check whether the coefficient of the highest-power term becomes zero.
Frequently asked questions
What is the correct answer to this question?
\(a=-7\)
Why is this the correct answer?
For the polynomial to have degree 2, the coefficient of \(x^6\) must be zero. Thus, \(a+7=0\), which gives \(a=-7\). For this value, the polynomial becomes \(-4x^2+9\), whose degree is 2. If \(a=0\), the coefficient of \(x^6\) is still 7, so the degree remains 6. Exam tip: First check whether the coefficient of the highest-power term becomes zero.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Degree of a Polynomial.
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