If a graph touches the x-axis at (4,0) and crosses it at (-2,0), what is the sum of the zeros?
Answer and explanation
Correct answer: 2
A touch at (4,0) means x=4 is a zero and a crossing at (-2,0) means x=-2 is a zero. Thus the sum of zeros is \(4+(-2)=2\). Closest distractor: 6 would result from incorrectly adding absolute values (4+2) and ignoring the sign; that is incorrect. Exam tip: a touch-point is still a root (often with even multiplicity), and you must include its value when summing zeros.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
A touch at (4,0) means x=4 is a zero and a crossing at (-2,0) means x=-2 is a zero. Thus the sum of zeros is \(4+(-2)=2\). Closest distractor: 6 would result from incorrectly adding absolute values (4+2) and ignoring the sign; that is incorrect. Exam tip: a touch-point is still a root (often with even multiplicity), and you must include its value when summing zeros.
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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