If p(x) = x² − 6x + 9, at which point will its graph touch the x-axis?
Answer and explanation
Correct answer: (3, 0)
To find where the graph touches the x-axis, set p(x) equal to zero. The polynomial can be written as x² − 6x + 9 = (x − 3)². Thus (x − 3)² = 0 gives x − 3 = 0, so x = 3. Because the factor is repeated, the quadratic has a repeated zero and the parabola touches the x-axis at that point rather than crossing it. The corresponding point has y-coordinate 0, so it is (3, 0). Therefore option B is correct. Option C confuses the constant term with the zero, while option D is the y-intercept, not the x-axis contact point.
Frequently asked questions
What is the correct answer to this question?
(3, 0)
Why is this the correct answer?
To find where the graph touches the x-axis, set p(x) equal to zero. The polynomial can be written as x² − 6x + 9 = (x − 3)². Thus (x − 3)² = 0 gives x − 3 = 0, so x = 3. Because the factor is repeated, the quadratic has a repeated zero and the parabola touches the x-axis at that point rather than crossing it. The corresponding point has y-coordinate 0, so it is (3, 0). Therefore option B is correct. Option C confuses the constant term with the zero, while option D is the y-intercept, not the x-axis contact point.
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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