If \(p(-1)<0\), \(p(0)<0\) and \(p(2)=0\), which of the given numbers is definitely a zero of the polynomial?
Answer and explanation
Correct answer: 2
By definition a number \(a\) is a zero of the polynomial only if \(p(a)=0\). Here \(p(2)=0\) is given, so 2 is definitely a root. The statements \(p(-1)<0\) and \(p(0)<0\) show values that are nonzero (negative), so \(-1\) and \(0\) are not roots. 'None' is incorrect because \(p(2)=0\) explicitly gives a zero. Exam tip: to confirm a zero, look for an explicit equality \(p(a)=0\); sign information alone (positive/negative) does not prove a root.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
By definition a number \(a\) is a zero of the polynomial only if \(p(a)=0\). Here \(p(2)=0\) is given, so 2 is definitely a root. The statements \(p(-1)<0\) and \(p(0)<0\) show values that are nonzero (negative), so \(-1\) and \(0\) are not roots. 'None' is incorrect because \(p(2)=0\) explicitly gives a zero. Exam tip: to confirm a zero, look for an explicit equality \(p(a)=0\); sign information alone (positive/negative) does not prove a root.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
