If the zeroes of x^2+px−3 are 2+√7 and 2−√7, what is p?
Answer and explanation
Correct answer: −4
For a monic quadratic x²+px−3, the sum of its zeroes is −p and the product is −3. Add the given zeroes: (2+√7)+(2−√7)=4, because the irrational terms cancel. Therefore −p=4, giving p=−4. The product provides an independent check: (2+√7)(2−√7)=2²−(√7)²=4−7=−3, exactly the constant term. Thus option A is correct. Option B uses the sum without reversing its sign, while options C and D confuse the constant term or its sign with the coefficient p. Both the sum and product relations confirm the answer.
Frequently asked questions
What is the correct answer to this question?
−4
Why is this the correct answer?
For a monic quadratic x²+px−3, the sum of its zeroes is −p and the product is −3. Add the given zeroes: (2+√7)+(2−√7)=4, because the irrational terms cancel. Therefore −p=4, giving p=−4. The product provides an independent check: (2+√7)(2−√7)=2²−(√7)²=4−7=−3, exactly the constant term. Thus option A is correct. Option B uses the sum without reversing its sign, while options C and D confuse the constant term or its sign with the coefficient p. Both the sum and product relations confirm the answer.
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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