If the graph of \(p(x)=x^2-11x+30\) is drawn, at which points does it intersect the x-axis?
Answer and explanation
Correct answer: (5,0) and (6,0)
Points on the x-axis have y-coordinate zero, so set \(p(x)=0\): \(x^2-11x+30=0\). Factorising gives \(x^2-11x+30=(x-5)(x-6)\), so the roots are \(x=5\) and \(x=6\). Thus the graph meets the x-axis at (5,0) and (6,0). The closest distractor (B) has the signs reversed; option C lists y-axis intercepts, and option D confuses coefficients with roots. Exam tip: set the polynomial equal to zero and factorise (or use the quadratic formula) to find x-intercepts quickly.
Frequently asked questions
What is the correct answer to this question?
(5,0) and (6,0)
Why is this the correct answer?
Points on the x-axis have y-coordinate zero, so set \(p(x)=0\): \(x^2-11x+30=0\). Factorising gives \(x^2-11x+30=(x-5)(x-6)\), so the roots are \(x=5\) and \(x=6\). Thus the graph meets the x-axis at (5,0) and (6,0). The closest distractor (B) has the signs reversed; option C lists y-axis intercepts, and option D confuses coefficients with roots. Exam tip: set the polynomial equal to zero and factorise (or use the quadratic formula) to find x-intercepts quickly.
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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