If the graph of a polynomial intersects the x-axis at \((0,0)\) and \((a,0)\), where \(a \neq 0\), what is the product of its zeros?
Answer and explanation
Correct answer: 0
The x-intercepts give the zeros of the polynomial: here the zeros are \(0\) and \(a\). Their product is \(0\times a=0\). The closest distractor, \(a\), incorrectly treats the product as the nonzero root alone; but a single zero root forces the whole product to be zero. Exam tip: whenever one root is 0, the product of the roots is 0 immediately.
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What is the correct answer to this question?
0
Why is this the correct answer?
The x-intercepts give the zeros of the polynomial: here the zeros are \(0\) and \(a\). Their product is \(0\times a=0\). The closest distractor, \(a\), incorrectly treats the product as the nonzero root alone; but a single zero root forces the whole product to be zero. Exam tip: whenever one root is 0, the product of the roots is 0 immediately.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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