If p(x) = 6x² − 72x + 216, how will the graph meet the x-axis?
Answer and explanation
Correct answer: It will touch the x-axis at x = 6.
To determine how the parabola meets the x-axis, factor the polynomial: 6x² − 72x + 216 = 6(x² − 12x + 36) = 6(x − 6)². The only zero is x = 6, and it is repeated twice. A quadratic with a repeated real zero touches the x-axis at that point rather than crossing it at two different points. Therefore the graph touches the x-axis at x = 6, so option A is correct. The factor 6 changes the vertical scale of the graph but does not change its zero. Hence x = −6 is incorrect, and the graph does meet the axis.
Frequently asked questions
What is the correct answer to this question?
It will touch the x-axis at x = 6.
Why is this the correct answer?
To determine how the parabola meets the x-axis, factor the polynomial: 6x² − 72x + 216 = 6(x² − 12x + 36) = 6(x − 6)². The only zero is x = 6, and it is repeated twice. A quadratic with a repeated real zero touches the x-axis at that point rather than crossing it at two different points. Therefore the graph touches the x-axis at x = 6, so option A is correct. The factor 6 changes the vertical scale of the graph but does not change its zero. Hence x = −6 is incorrect, and the graph does meet the axis.
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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