If \(p(x)=x^2-hx\), what are the x-intercepts of its graph?
Answer and explanation
Correct answer: (0,0), (h,0)
Factor: \(p(x)=x^2-hx=x(x-h)\). X-intercepts occur when \(p(x)=0\), so \(x=0\) or \(x=h\). Thus the intercepts are (0,0) and (h,0). Choice B is wrong due to sign (root is \(h\), not \(-h\)); choice D is invalid because (0,h) is not on the x-axis (y≠0). Exam tip: set \(p(x)=0\) or factor out the common \(x\); the roots give the x-coordinates of intercepts.
Frequently asked questions
What is the correct answer to this question?
(0,0), (h,0)
Why is this the correct answer?
Factor: \(p(x)=x^2-hx=x(x-h)\). X-intercepts occur when \(p(x)=0\), so \(x=0\) or \(x=h\). Thus the intercepts are (0,0) and (h,0). Choice B is wrong due to sign (root is \(h\), not \(-h\)); choice D is invalid because (0,h) is not on the x-axis (y≠0). Exam tip: set \(p(x)=0\) or factor out the common \(x\); the roots give the x-coordinates of intercepts.
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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