If the graph of a polynomial cuts the x-axis at the points (-4,0) and (4,0), which statement about the zeroes is correct?
Answer and explanation
Correct answer: They are opposites of each other
The x-intercepts give the zeros of the polynomial; here the zeros are -4 and 4. They have equal magnitude and opposite signs, so they are opposites of each other. In fact their sum is zero: \(\alpha+\beta=0\) (with \(\alpha=-4,\beta=4\)). The closest distractor A is wrong because "both equal" would mean the same number (e.g. 4 and 4), which is not the case. Exam tip: read the x-coordinates of intercepts as the zeros and compare their signs and magnitudes directly.
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What is the correct answer to this question?
They are opposites of each other
Why is this the correct answer?
The x-intercepts give the zeros of the polynomial; here the zeros are -4 and 4. They have equal magnitude and opposite signs, so they are opposites of each other. In fact their sum is zero: \(\alpha+\beta=0\) (with \(\alpha=-4,\beta=4\)). The closest distractor A is wrong because "both equal" would mean the same number (e.g. 4 and 4), which is not the case. Exam tip: read the x-coordinates of intercepts as the zeros and compare their signs and magnitudes directly.
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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