If x² − 5x = 0 is divided by x and only x − 5 = 0 is written, which root is missed?
Answer and explanation
Correct answer: x = 0
The governing principle is that dividing an equation by a variable factor can discard a solution when that factor itself may be zero. The original equation factors as x² − 5x = x(x − 5) = 0. By the zero-product property, either x = 0 or x − 5 = 0, which gives x = 5. If we divide by x immediately, we implicitly assume x is not zero and obtain only x − 5 = 0. Thus the root x = 0 is lost. Option A is correct. The root x = 5 is retained, while −5 and 1 do not satisfy the original equation. The safe method is to factor first and consider every factor separately.
Frequently asked questions
What is the correct answer to this question?
x = 0
Why is this the correct answer?
The governing principle is that dividing an equation by a variable factor can discard a solution when that factor itself may be zero. The original equation factors as x² − 5x = x(x − 5) = 0. By the zero-product property, either x = 0 or x − 5 = 0, which gives x = 5. If we divide by x immediately, we implicitly assume x is not zero and obtain only x − 5 = 0. Thus the root x = 0 is lost. Option A is correct. The root x = 5 is retained, while −5 and 1 do not satisfy the original equation. The safe method is to factor first and consider every factor separately.
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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