If \(p(x)=x^2-(m+n)x+mn\), what are the x-axis intersections (x-intercepts) of its graph?
Answer and explanation
Correct answer: (m,0) and (n,0)
Factor the polynomial: \(p(x)=x^2-(m+n)x+mn=(x-m)(x-n)\). Hence the roots are \(x=m\) and \(x=n\), so the x-intercepts are (m,0) and (n,0). Closest distractor (\(-m,0\),\(-n,0\)) is incorrect because the signs are negated; (0,m),(0,n) are y-intercepts; (m,n) are arbitrary coordinate points and do not represent roots. Exam tip: set \(p(x)=0\) or factorize to find roots, then report each root as (root,0).
Frequently asked questions
What is the correct answer to this question?
(m,0) and (n,0)
Why is this the correct answer?
Factor the polynomial: \(p(x)=x^2-(m+n)x+mn=(x-m)(x-n)\). Hence the roots are \(x=m\) and \(x=n\), so the x-intercepts are (m,0) and (n,0). Closest distractor (\(-m,0\),\(-n,0\)) is incorrect because the signs are negated; (0,m),(0,n) are y-intercepts; (m,n) are arbitrary coordinate points and do not represent roots. Exam tip: set \(p(x)=0\) or factorize to find roots, then report each root as (root,0).
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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