If the sum of zeroes is 2√5 and the product is 4, which is a monic quadratic polynomial?
Answer and explanation
Correct answer: x² − 2√5x + 4
A monic quadratic with zeroes α and β has leading coefficient 1 and is written as x² − (α + β)x + αβ. The given sum is α + β = 2√5 and the product is αβ = 4. Substitution therefore gives x² − 2√5x + 4. This is exactly option A. Option B has the wrong sign for the sum, while option C places the given sum and product in the wrong coefficients. Option D has both an incorrect sign arrangement and an incorrect constant term. The fact that the sum is irrational is acceptable; a polynomial may have irrational coefficients.
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What is the correct answer to this question?
x² − 2√5x + 4
Why is this the correct answer?
A monic quadratic with zeroes α and β has leading coefficient 1 and is written as x² − (α + β)x + αβ. The given sum is α + β = 2√5 and the product is αβ = 4. Substitution therefore gives x² − 2√5x + 4. This is exactly option A. Option B has the wrong sign for the sum, while option C places the given sum and product in the wrong coefficients. Option D has both an incorrect sign arrangement and an incorrect constant term. The fact that the sum is irrational is acceptable; a polynomial may have irrational coefficients.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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