If one root of x² + ax + 18 = 0 is 2, what are the other root and a?
Answer and explanation
Correct answer: Other root 9, a = −11
Let the second root be s. For a monic quadratic x² + ax + 18 = 0, the product of the roots equals the constant term, so 2s = 18 and therefore s = 9. The sum of the roots is the negative of the coefficient of x: 2 + 9 = −a. Thus 11 = −a, giving a = −11. The result can also be verified directly by substituting the known root x = 2: 2² + (−11)(2) + 18 = 4 − 22 + 18 = 0. Option B has the wrong second-root sign and coefficient, while option C has the correct second root but the wrong sign of a. Option D does not satisfy the product relation. Hence option A is the only correct pair.
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What is the correct answer to this question?
Other root 9, a = −11
Why is this the correct answer?
Let the second root be s. For a monic quadratic x² + ax + 18 = 0, the product of the roots equals the constant term, so 2s = 18 and therefore s = 9. The sum of the roots is the negative of the coefficient of x: 2 + 9 = −a. Thus 11 = −a, giving a = −11. The result can also be verified directly by substituting the known root x = 2: 2² + (−11)(2) + 18 = 4 − 22 + 18 = 0. Option B has the wrong second-root sign and coefficient, while option C has the correct second root but the wrong sign of a. Option D does not satisfy the product relation. Hence option A is the only correct pair.
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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