If the x-axis intersections of a graph are (0,0), (d,0), (−d,0), where \(d\neq0\), what is the product of the zeros?
Answer and explanation
Correct answer: \(0\)
The x-coordinates of the x-intercepts are the polynomial's zeros: 0, d and −d. Their product is 0\times d\times(−d)=0 because any product containing 0 equals 0. Note that \(d\neq0\) ensures the other two zeros are nonzero, but the presence of the zero root makes the whole product zero. The closest distractor, \(-d^2\), would be the product of d and −d alone and is wrong because it ignores the zero root. Exam tip: always check intercepts for a root equal to 0 first — it instantly gives the product as 0.
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
The x-coordinates of the x-intercepts are the polynomial's zeros: 0, d and −d. Their product is 0\times d\times(−d)=0 because any product containing 0 equals 0. Note that \(d\neq0\) ensures the other two zeros are nonzero, but the presence of the zero root makes the whole product zero. The closest distractor, \(-d^2\), would be the product of d and −d alone and is wrong because it ignores the zero root. Exam tip: always check intercepts for a root equal to 0 first — it instantly gives the product as 0.
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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