If p(x)=x²−2√6x+5, what are the product and sum of its zeroes?
Answer and explanation
Correct answer: Product 5, sum 2√6
Use Vieta’s relations for a quadratic ax²+bx+c. If its zeroes are α and β, then α+β=−b/a and αβ=c/a. In p(x)=x²−2√6x+5, the coefficients are a=1, b=−2√6, and c=5. Hence the sum is −(−2√6)/1=2√6, while the product is 5/1=5. Thus option A gives both values in the requested order. Option B interchanges the sum and product. Option C incorrectly changes the sign of the product even though the constant term is positive. Option D forgets the negative sign in the formula for the sum. Individual roots are unnecessary because the coefficient relations answer the question directly.
Frequently asked questions
What is the correct answer to this question?
Product 5, sum 2√6
Why is this the correct answer?
Use Vieta’s relations for a quadratic ax²+bx+c. If its zeroes are α and β, then α+β=−b/a and αβ=c/a. In p(x)=x²−2√6x+5, the coefficients are a=1, b=−2√6, and c=5. Hence the sum is −(−2√6)/1=2√6, while the product is 5/1=5. Thus option A gives both values in the requested order. Option B interchanges the sum and product. Option C incorrectly changes the sign of the product even though the constant term is positive. Option D forgets the negative sign in the formula for the sum. Individual roots are unnecessary because the coefficient relations answer the question directly.
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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