If x = −3 is a root of 2x² + rx − 9 = 0, what is r?
Answer and explanation
Correct answer: 3
The governing principle is that every root satisfies the equation. Since x = −3 is a root, substitute −3 into 2x² + rx − 9 = 0: 2(−3)² + r(−3) − 9 = 0. This simplifies to 2(9) − 3r − 9 = 0, so 18 − 3r − 9 = 0, or 9 − 3r = 0. Hence 3r = 9 and r = 3. Therefore option A is correct. The most likely error is to write r(−3) as +3r, which leads to an incorrect sign. Options C and D do not satisfy the original equation when x = −3 is substituted. Direct verification with r = 3 gives 18 − 9 − 9 = 0.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The governing principle is that every root satisfies the equation. Since x = −3 is a root, substitute −3 into 2x² + rx − 9 = 0: 2(−3)² + r(−3) − 9 = 0. This simplifies to 2(9) − 3r − 9 = 0, so 18 − 3r − 9 = 0, or 9 − 3r = 0. Hence 3r = 9 and r = 3. Therefore option A is correct. The most likely error is to write r(−3) as +3r, which leads to an incorrect sign. Options C and D do not satisfy the original equation when x = −3 is substituted. Direct verification with r = 3 gives 18 − 9 − 9 = 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
