A student saw the point (0, −6) and wrote −6 as a zero (root) of a function. Why is this incorrect?
Answer and explanation
Correct answer: Because it is a y-axis intercept and at this point y ≠ 0
A root (zero) is an x‑value where the function equals zero (the point lies on the x‑axis). At (0, −6) the y‑value is −6, so the point is a y‑intercept (x = 0, y ≠ 0), not an x‑intercept. Hence −6 is the y‑value, not a root. Why other choices are wrong: B is incorrect because sign alone does not prevent a number being a root — roots can be negative, positive or zero. C is incorrect because x = 0 is not automatically a root; only if f(0) = 0. D is false because not every point gives y = 0. Exam tip: always check which coordinate is x and which is y; zeros correspond to x‑coordinates where y = 0 (x‑axis intersections).
Frequently asked questions
What is the correct answer to this question?
Because it is a y-axis intercept and at this point y ≠ 0
Why is this the correct answer?
A root (zero) is an x‑value where the function equals zero (the point lies on the x‑axis). At (0, −6) the y‑value is −6, so the point is a y‑intercept (x = 0, y ≠ 0), not an x‑intercept. Hence −6 is the y‑value, not a root. Why other choices are wrong: B is incorrect because sign alone does not prevent a number being a root — roots can be negative, positive or zero. C is incorrect because x = 0 is not automatically a root; only if f(0) = 0. D is false because not every point gives y = 0. Exam tip: always check which coordinate is x and which is y; zeros correspond to x‑coordinates where y = 0 (x‑axis intersections).
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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