If p(x) = 5x^2 - 50x + 125, how will the graph meet the x-axis?
Answer and explanation
Correct answer: It will touch the x-axis at x = 5
The graph behavior follows from the multiplicity of the real zero. Factor the polynomial: 5x^2 - 50x + 125 = 5(x^2 - 10x + 25) = 5(x - 5)^2. Thus the only zero is x = 5, repeated twice. A parabola with a repeated real zero reaches the x-axis at that point and turns back, so it touches rather than crosses the axis. Therefore option A is correct. Option B uses the wrong sign for the root. Option C would be appropriate if the quadratic had two distinct real roots, and option D would be appropriate only if the quadratic had no real roots. The non-zero factor 5 changes vertical scaling but does not change the zero.
Frequently asked questions
What is the correct answer to this question?
It will touch the x-axis at x = 5
Why is this the correct answer?
The graph behavior follows from the multiplicity of the real zero. Factor the polynomial: 5x^2 - 50x + 125 = 5(x^2 - 10x + 25) = 5(x - 5)^2. Thus the only zero is x = 5, repeated twice. A parabola with a repeated real zero reaches the x-axis at that point and turns back, so it touches rather than crosses the axis. Therefore option A is correct. Option B uses the wrong sign for the root. Option C would be appropriate if the quadratic had two distinct real roots, and option D would be appropriate only if the quadratic had no real roots. The non-zero factor 5 changes vertical scaling but does not change the zero.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
