If p(x) = 4x^2 - 24x + 36, how will the graph meet the x-axis?
Answer and explanation
Correct answer: It will touch the x-axis at x = 3
The relevant principle is that a repeated real zero makes a parabola touch the x-axis, whereas two distinct real zeroes make it cross at two points. Factor the expression: 4x^2 - 24x + 36 = 4(x^2 - 6x + 9) = 4(x - 3)^2. Thus the discriminant is zero and the only zero is x = 3, repeated twice. The graph therefore touches the x-axis at (3, 0). Option A is correct. Option B results from reversing the sign, option C would require a positive discriminant and two different roots, and option D would require a negative discriminant with no real roots.
Frequently asked questions
What is the correct answer to this question?
It will touch the x-axis at x = 3
Why is this the correct answer?
The relevant principle is that a repeated real zero makes a parabola touch the x-axis, whereas two distinct real zeroes make it cross at two points. Factor the expression: 4x^2 - 24x + 36 = 4(x^2 - 6x + 9) = 4(x - 3)^2. Thus the discriminant is zero and the only zero is x = 3, repeated twice. The graph therefore touches the x-axis at (3, 0). Option A is correct. Option B results from reversing the sign, option C would require a positive discriminant and two different roots, and option D would require a negative discriminant with no real roots.
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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