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Class 10MathematicsPolynomialsPolynomials in one variableHardLevel 47
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If \\(f(x)=x^2+px+q\\) is a quadratic polynomial and \\(f(0)=6\\) and \\(f(2)=0\\), what is the value of the coefficient \\(p\\)?

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Answer and explanation

Correct answer: -5

Since \\(f(0)=q=6\\), the condition \\(f(2)=0\\) gives \\(2^2+2p+6=0\\). Thus, \\(4+2p+6=0\\), so \\(2p=-10\\) and \\(p=-5\\). Exam tip: use the value at \\(x=0\\) first to determine the constant term, then apply the second condition.

Related tags

Quadratic PolynomialPolynomial EvaluationCoefficientsConstant Term

Frequently asked questions

What is the correct answer to this question?

-5

Why is this the correct answer?

Since \\(f(0)=q=6\\), the condition \\(f(2)=0\\) gives \\(2^2+2p+6=0\\). Thus, \\(4+2p+6=0\\), so \\(2p=-10\\) and \\(p=-5\\). Exam tip: use the value at \\(x=0\\) first to determine the constant term, then apply the second condition.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.

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  1. 1If (p(x)=x^2-8x+10), what are its zeroes?
  2. 2Which option is the simplified form of (x^8 - 81) / (x^4 - 9), where x^4 ≠ 9?
  3. 3Which expression is a polynomial in one variable (x)?
  4. 4What is the degree of the polynomial p(x) = 4x^3 − 2x + 9?
  5. 5What is the constant term of the polynomial \(7x^2+5x-11\)?
  6. 6What is the coefficient of x^2 in 5x^4 − 3x^2 + x − 6?
  7. 7Which polynomial is a quadratic polynomial?
  8. 8Which expression is not a polynomial?
  9. 9For the polynomial \(p(x)=2x^2-3x+1\), what is the value of \(p(1)\)?
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