If \(p(x)=x^2-10x+25\), how does its graph meet the x-axis?
Answer and explanation
Correct answer: It will touch at \(x=5\)
Factorize: \(p(x)=x^2-10x+25=(x-5)^2\). The root \(x=5\) has multiplicity 2 (a repeated zero), so the parabola touches the x-axis at a single point and does not cross it. Closest distractor C is incorrect because cutting at two distinct points requires two distinct real roots (discriminant > 0). Exam tip: if the discriminant \(b^2-4ac=0\), the quadratic has a repeated root and the graph is tangent to the x-axis.
Frequently asked questions
What is the correct answer to this question?
It will touch at \(x=5\)
Why is this the correct answer?
Factorize: \(p(x)=x^2-10x+25=(x-5)^2\). The root \(x=5\) has multiplicity 2 (a repeated zero), so the parabola touches the x-axis at a single point and does not cross it. Closest distractor C is incorrect because cutting at two distinct points requires two distinct real roots (discriminant > 0). Exam tip: if the discriminant \(b^2-4ac=0\), the quadratic has a repeated root and the graph is tangent to the x-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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