If the polynomial \(f(x)=x^3+ax+b\) satisfies \(f(1)=4\) and \(f(-1)=-2\), what is the value of \(a\)?
Answer and explanation
Correct answer: 2
Using \(f(1)=4\), we get \(1+a+b=4\), so \(a+b=3\). Using \(f(-1)=-2\), we get \(-1-a+b=-2\), so \(-a+b=-1\). Subtracting the second equation from the first gives \(2a=4\), hence \(a=2\). Therefore, option B is correct. Exam tip: when values at \(1\) and \(-1\) are given, substitute them directly and eliminate the common constant term.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Using \(f(1)=4\), we get \(1+a+b=4\), so \(a+b=3\). Using \(f(-1)=-2\), we get \(-1-a+b=-2\), so \(-a+b=-1\). Subtracting the second equation from the first gives \(2a=4\), hence \(a=2\). Therefore, option B is correct. Exam tip: when values at \(1\) and \(-1\) are given, substitute them directly and eliminate the common constant term.
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.
