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Class 10MathematicsPolynomialsPolynomials in one variableExpertLevel 48
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If the difference between the two zeroes of the polynomial \(p(x)=x^2-6x+s\) is 2, what is the value of \(s\)?

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Answer and explanation

Correct answer: 8

Let the two zeroes be \(t\) and \(t+2\). Their sum is \(6\), so \(t+(t+2)=6\), giving \(t=2\) and the other zero as \(4\). The product of the zeroes equals \(s\); hence, \(s=2\times4=8\). Exam tip: For \(x^2+bx+c\), the sum of the zeroes is \(-b\) and their product is \(c\).

Related tags

PolynomialsZeroes Of PolynomialsQuadratic PolynomialVieta Relations

Frequently asked questions

What is the correct answer to this question?

8

Why is this the correct answer?

Let the two zeroes be \(t\) and \(t+2\). Their sum is \(6\), so \(t+(t+2)=6\), giving \(t=2\) and the other zero as \(4\). The product of the zeroes equals \(s\); hence, \(s=2\times4=8\). Exam tip: For \(x^2+bx+c\), the sum of the zeroes is \(-b\) and their product is \(c\).

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)=x²−8x+10), what are its zeroes?
  2. 2If p(x) = 2x² − 4√2x + 4, what is the sum of its zeroes?
  3. 3If the sum of zeroes is 2√5 and the product is 4, which is a monic quadratic polynomial?
  4. 4If √2 and √8 are zeroes of a quadratic polynomial, what is the sum of the zeroes?
  5. 5If p(x) = x² − 2√2x + 2, which is the correct factorized form of p(x)?
  6. 6Which polynomial has rational coefficients and zeroes 1 + √2 and 1 − √2?
  7. 7Which option is the simplified form of (x^8 - 81) / (x^4 - 9), where x^4 ≠ 9?
  8. 8Which expression is a polynomial in one variable (x)?
  9. 9What is the degree of the polynomial p(x) = 4x^3 − 2x + 9?
  10. 10What is the constant term of the polynomial \(7x^2+5x-11\)?
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