If p(x)=x^2−2x−3√2, what does the constant term tell about the zeroes?
Answer and explanation
Correct answer: The product of zeroes is −3√2
For a quadratic ax²+bx+c with zeroes α and β, Vieta’s relation gives αβ=c/a. Here a=1 and the constant term c=−3√2, so αβ=(−3√2)/1=−3√2. Thus option A is correct. The sum is a separate relation, α+β=−b/a=2, so the constant term does not represent the sum. The discriminant is b²−4ac, which here is 4+12√2, not −3√2. Also, knowing an irrational product alone does not establish that both zeroes are rational; in fact their nature would require further analysis. The coefficient is monic, which makes the constant term directly equal to the product.
Frequently asked questions
What is the correct answer to this question?
The product of zeroes is −3√2
Why is this the correct answer?
For a quadratic ax²+bx+c with zeroes α and β, Vieta’s relation gives αβ=c/a. Here a=1 and the constant term c=−3√2, so αβ=(−3√2)/1=−3√2. Thus option A is correct. The sum is a separate relation, α+β=−b/a=2, so the constant term does not represent the sum. The discriminant is b²−4ac, which here is 4+12√2, not −3√2. Also, knowing an irrational product alone does not establish that both zeroes are rational; in fact their nature would require further analysis. The coefficient is monic, which makes the constant term directly equal to the product.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
