If the zeroes of x^2−2x+m are 1+√6 and 1−√6, what is m?
Answer and explanation
Correct answer: −5
For a monic quadratic x²+bx+c, the product of the zeroes equals c. The given zeroes are conjugates, so their product can be calculated using (a+b)(a−b)=a²−b². Thus (1+√6)(1−√6)=1²−(√6)²=1−6=−5. Consequently the constant term m must be −5. The sum also checks the data: (1+√6)+(1−√6)=2, and the coefficient of x is −2, equal to the negative of that sum. Therefore option A is correct. Option B ignores the negative result, while 7 and −7 come from incorrect addition or multiplication of the radical terms.
Frequently asked questions
What is the correct answer to this question?
−5
Why is this the correct answer?
For a monic quadratic x²+bx+c, the product of the zeroes equals c. The given zeroes are conjugates, so their product can be calculated using (a+b)(a−b)=a²−b². Thus (1+√6)(1−√6)=1²−(√6)²=1−6=−5. Consequently the constant term m must be −5. The sum also checks the data: (1+√6)+(1−√6)=2, and the coefficient of x is −2, equal to the negative of that sum. Therefore option A is correct. Option B ignores the negative result, while 7 and −7 come from incorrect addition or multiplication of the radical terms.
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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