If p(x)=2x^2+12x+18, how will the graph meet the x-axis?
Answer and explanation
Correct answer: It will touch at x=-3
The governing idea is that the real zeroes determine where a polynomial graph meets the x-axis, and a repeated zero generally means the graph touches the axis without crossing it. Factor the polynomial: 2x^2+12x+18 = 2(x^2+6x+9) = 2(x+3)^2. Hence the only zero is x=-3, with multiplicity two. Since the square is never negative and the leading factor is positive, the graph has its minimum value 0 at x=-3 and touches the x-axis there. Option A is correct. Option B has the wrong sign, Option C would require two distinct real zeroes, and Option D ignores the real repeated zero.
Frequently asked questions
What is the correct answer to this question?
It will touch at x=-3
Why is this the correct answer?
The governing idea is that the real zeroes determine where a polynomial graph meets the x-axis, and a repeated zero generally means the graph touches the axis without crossing it. Factor the polynomial: 2x^2+12x+18 = 2(x^2+6x+9) = 2(x+3)^2. Hence the only zero is x=-3, with multiplicity two. Since the square is never negative and the leading factor is positive, the graph has its minimum value 0 at x=-3 and touches the x-axis there. Option A is correct. Option B has the wrong sign, Option C would require two distinct real zeroes, and Option D ignores the real repeated 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..
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