If the roots of a monic quadratic equation are r and 3r, and their sum is 16, what is the constant term?
Answer and explanation
Correct answer: 48
Because the roots are r and 3r, their sum is r + 3r = 4r. The given sum 16 therefore gives 4r = 16, so r = 4. The roots are consequently 4 and 12. For a monic quadratic, the constant term is the product of the roots, since the equation is x² − (sum of roots)x + (product of roots) = 0. Thus the constant term is 4 × 12 = 48. Option B is only the sum, not the product; 64 and 32 do not represent the product of the two roots. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
48
Why is this the correct answer?
Because the roots are r and 3r, their sum is r + 3r = 4r. The given sum 16 therefore gives 4r = 16, so r = 4. The roots are consequently 4 and 12. For a monic quadratic, the constant term is the product of the roots, since the equation is x² − (sum of roots)x + (product of roots) = 0. Thus the constant term is 4 × 12 = 48. Option B is only the sum, not the product; 64 and 32 do not represent the product of the two roots. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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