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Class 9MathematicsIntroduction to PolynomialsLinear polynomialsExpertLevel 32
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If (p(x)=mx+n) and (p(-3)=p(1)), when can (p(x)) be linear?

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Answer and explanation

Correct answer: Never

Using \(p(-3)=p(1)\), we get \(-3m+n=m+n\). Hence, \(-4m=0\), so \(m=0\). Then \(p(x)=n\), which is a constant polynomial, not a linear polynomial. Whether \(n=0\) or not does not change this conclusion. Exam tip: for \(mx+n\) to be linear, \(m\ne0\) is essential.

Related tags

PolynomialsLinear PolynomialsConstant PolynomialAlgebraic ConditionsClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

Never

Why is this the correct answer?

Using \(p(-3)=p(1)\), we get \(-3m+n=m+n\). Hence, \(-4m=0\), so \(m=0\). Then \(p(x)=n\), which is a constant polynomial, not a linear polynomial. Whether \(n=0\) or not does not change this conclusion. Exam tip: for \(mx+n\) to be linear, \(m\ne0\) is essential.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.

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10 more MCQs
  1. 1If the highest power in a polynomial is 1, what is it called?
  2. 2Which expression is not a linear polynomial?
  3. 3Which expression is a polynomial but not a linear polynomial?
  4. 4Which statement is correct about the zeroes of a non-zero linear polynomial?
  5. 5Which expression is a polynomial in (s) and has degree (1)?
  6. 6If \(p(x)=ax+b\), where \(a\ne0\), is a linear polynomial, which property of its graph is always true?
  7. 7Which of the following expressions is a linear polynomial in \(x\)?
  8. 8A taxi charges a fixed fee of ₹50 and ₹12 per kilometre. If the distance travelled is represented by \(x\), which statement about \(C(x)=12x+50\) is correct?
  9. 9What type of polynomial is (4x-9)?
  10. 10What is the degree of a linear polynomial?
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