If the graph of a polynomial intersects the x-axis at the points (0,0), (2,0) and (5,0), which statement is correct?
Answer and explanation
Correct answer: 0, 2 and 5 are zeros
If a graph meets the x-axis at (a,0), then x=a is a root of the polynomial because the polynomial's value is 0 there. Since the graph passes through (0,0), (2,0) and (5,0), the polynomial equals zero at x=0, x=2 and x=5; hence all three are zeros. Closest distractor: option D wrongly omits x=0; options A and C ignore the given x-intercepts. Exam tip: any x-intercept (a,0) directly gives a root x=a — never overlook the origin (0,0).
Frequently asked questions
What is the correct answer to this question?
0, 2 and 5 are zeros
Why is this the correct answer?
If a graph meets the x-axis at (a,0), then x=a is a root of the polynomial because the polynomial's value is 0 there. Since the graph passes through (0,0), (2,0) and (5,0), the polynomial equals zero at x=0, x=2 and x=5; hence all three are zeros. Closest distractor: option D wrongly omits x=0; options A and C ignore the given x-intercepts. Exam tip: any x-intercept (a,0) directly gives a root x=a — never overlook the origin (0,0).
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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