If \(p(x)=x^2-2kx+k^2\), at which x-value will its graph touch the x-axis?
Answer and explanation
Correct answer: x = k
Factor the polynomial: \(p(x)=x^2-2kx+k^2=(x-k)^2\). Hence the root is repeated at \(x=k\), so the graph touches (but does not cross) the x-axis at \(x=k\). The distractor \(x=-k\) is incorrect because it is not a root of \((x-k)^2\). Exam tip: recognize perfect-square trinomials quickly, or check the discriminant \(b^2-4ac=0\) to identify a repeated root.
Frequently asked questions
What is the correct answer to this question?
x = k
Why is this the correct answer?
Factor the polynomial: \(p(x)=x^2-2kx+k^2=(x-k)^2\). Hence the root is repeated at \(x=k\), so the graph touches (but does not cross) the x-axis at \(x=k\). The distractor \(x=-k\) is incorrect because it is not a root of \((x-k)^2\). Exam tip: recognize perfect-square trinomials quickly, or check the discriminant \(b^2-4ac=0\) to identify a repeated root.
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.
