If p(x)=x^2−6√2x+17, what are the sum and product of its zeroes?
Answer and explanation
Correct answer: Sum 6√2, product 17
For a quadratic ax²+bx+c, the sum of the zeroes is −b/a and their product is c/a. In p(x)=x²−6√2x+17, the coefficients are a=1, b=−6√2 and c=17. Therefore the sum is −(−6√2)/1=6√2, and the product is 17/1=17. Hence option A is correct. The negative sign in the x-coefficient must be reversed when finding the sum, which rules out option B. Options C and D interchange the roles of coefficients or use an incorrect sign for the constant term. These relations apply regardless of whether the coefficients are rational or irrational.
Frequently asked questions
What is the correct answer to this question?
Sum 6√2, product 17
Why is this the correct answer?
For a quadratic ax²+bx+c, the sum of the zeroes is −b/a and their product is c/a. In p(x)=x²−6√2x+17, the coefficients are a=1, b=−6√2 and c=17. Therefore the sum is −(−6√2)/1=6√2, and the product is 17/1=17. Hence option A is correct. The negative sign in the x-coefficient must be reversed when finding the sum, which rules out option B. Options C and D interchange the roles of coefficients or use an incorrect sign for the constant term. These relations apply regardless of whether the coefficients are rational or irrational.
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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