If \(p(x)=(x-6)^2\), what will the graph do with the x-axis?
Answer and explanation
Correct answer: It will touch at \(x=6\)
In \(p(x)=(x-6)^2\) the root \(x=6\) has multiplicity 2 (a repeated root). An even multiplicity causes the graph to touch the x-axis and turn back, so the curve touches at \(x=6\). Option B is wrong due to the wrong sign; option C would require two distinct real roots, not a repeated one; option D is wrong because a real root exists. Exam tip: even multiplicity → touch/turn, odd multiplicity → cross the axis.
Frequently asked questions
What is the correct answer to this question?
It will touch at \(x=6\)
Why is this the correct answer?
In \(p(x)=(x-6)^2\) the root \(x=6\) has multiplicity 2 (a repeated root). An even multiplicity causes the graph to touch the x-axis and turn back, so the curve touches at \(x=6\). Option B is wrong due to the wrong sign; option C would require two distinct real roots, not a repeated one; option D is wrong because a real root exists. Exam tip: even multiplicity → touch/turn, odd multiplicity → cross 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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