If \(p(x)=x^3+ax^2+bx\) satisfies \(p(0)=0\), which of the following conclusions is certainly correct?
Answer and explanation
Correct answer: 0 is a zero of \(p(x)\)
The equation \(p(0)=0\) directly means that \(x=0\) is a zero of the polynomial \(p(x)\). In fact, \(p(x)=x(x^2+ax+b)\), so \(x\) is a factor. This does not require \(a=0\) or \(b=0\); also, \(p(1)=1+a+b\), so 1 need not be a zero. Exam tip: If the constant term of a polynomial is zero, then zero is one of its zeros.
Frequently asked questions
What is the correct answer to this question?
0 is a zero of \(p(x)\)
Why is this the correct answer?
The equation \(p(0)=0\) directly means that \(x=0\) is a zero of the polynomial \(p(x)\). In fact, \(p(x)=x(x^2+ax+b)\), so \(x\) is a factor. This does not require \(a=0\) or \(b=0\); also, \(p(1)=1+a+b\), so 1 need not be a zero. Exam tip: If the constant term of a polynomial is zero, then zero is one of its zeros.
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.
