If 2+√13 is one zero of a quadratic polynomial with rational coefficients, what can the coefficient of x be?
Answer and explanation
Correct answer: −4
For a quadratic with rational coefficients, an irrational zero of the form a+b√d must be accompanied by its conjugate a−b√d. Therefore, if one zero is 2+√13, the other is 2−√13. Their sum is (2+√13)+(2−√13)=4. For a monic quadratic x²+Bx+C, the sum of zeroes equals −B, so B=−4. Equivalently, the polynomial is (x−2−√13)(x−2+√13)=x²−4x−9, whose x-coefficient is −4. Option A is correct; option B has the wrong sign, and C and D are not the required rational coefficient.
Frequently asked questions
What is the correct answer to this question?
−4
Why is this the correct answer?
For a quadratic with rational coefficients, an irrational zero of the form a+b√d must be accompanied by its conjugate a−b√d. Therefore, if one zero is 2+√13, the other is 2−√13. Their sum is (2+√13)+(2−√13)=4. For a monic quadratic x²+Bx+C, the sum of zeroes equals −B, so B=−4. Equivalently, the polynomial is (x−2−√13)(x−2+√13)=x²−4x−9, whose x-coefficient is −4. Option A is correct; option B has the wrong sign, and C and D are not the required rational coefficient.
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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