If a graph cuts the x-axis at x = -5, which of the following statements is correct?
Answer and explanation
Correct answer: -5 is a zero of the polynomial
The x-coordinate where a graph meets the x-axis is a root of the polynomial because at that point the function value is zero. So if the graph cuts at x = -5, then the polynomial satisfies \(f(-5)=0\) and -5 is a zero. Option B (5) is a common trap — the sign matters, +5 would be a root only if the graph crossed at x = 5. Options C and D contradict the given point of intersection. Exam tip: always read the x-coordinate of the intercept (including its sign); that x-value is the zero of the polynomial.
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What is the correct answer to this question?
-5 is a zero of the polynomial
Why is this the correct answer?
The x-coordinate where a graph meets the x-axis is a root of the polynomial because at that point the function value is zero. So if the graph cuts at x = -5, then the polynomial satisfies \(f(-5)=0\) and -5 is a zero. Option B (5) is a common trap — the sign matters, +5 would be a root only if the graph crossed at x = 5. Options C and D contradict the given point of intersection. Exam tip: always read the x-coordinate of the intercept (including its sign); that x-value is the zero of the polynomial.
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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