If a graph touches the x-axis at (7,0) and crosses it at (-4,0), what is the sum of the zeroes?
Answer and explanation
Correct answer: 3
Zeroes are the x-values where the graph meets the x‑axis. From (7,0) and (−4,0) the zeroes are 7 and −4, so their sum is 7 + (−4) = 3. ‘‘Touches’’ indicates an even multiplicity and ‘‘crosses’’ an odd multiplicity, but the zero values remain 7 and −4 — standard exam questions treat these zeroes once each unless multiplicity is explicitly requested. Closest distractor: −3 is simply the wrong sign; 11 and −11 arise from arithmetic errors. Exam tip: count every x‑intercept as a zero; only account for multiplicity if the question asks for sum with multiplicity.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Zeroes are the x-values where the graph meets the x‑axis. From (7,0) and (−4,0) the zeroes are 7 and −4, so their sum is 7 + (−4) = 3. ‘‘Touches’’ indicates an even multiplicity and ‘‘crosses’’ an odd multiplicity, but the zero values remain 7 and −4 — standard exam questions treat these zeroes once each unless multiplicity is explicitly requested. Closest distractor: −3 is simply the wrong sign; 11 and −11 arise from arithmetic errors. Exam tip: count every x‑intercept as a zero; only account for multiplicity if the question asks for sum with multiplicity.
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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