If \(p(x)=3x-15\), what is the x-axis intersection (x-intercept) of its graph?
Answer and explanation
Correct answer: (5,0)
The x-intercept occurs where the polynomial equals zero, i.e. \(p(x)=0\). Solving \(3x-15=0\) gives \(x=5\), so the intercept is \((5,0)\). Option \((0,-15)\) is the y-intercept (when \(x=0\), \(p(0)=-15\)), not the x-intercept. Options \((3,0)\) and \((-5,0)\) are simple arithmetic/sign errors — \((3,0)\) would arise from an incorrect solution and \((-5,0)\) flips the sign. Exam tip: for a linear polynomial \(ax+b\), the x-intercept is \((-b/a,0)\).
Frequently asked questions
What is the correct answer to this question?
(5,0)
Why is this the correct answer?
The x-intercept occurs where the polynomial equals zero, i.e. \(p(x)=0\). Solving \(3x-15=0\) gives \(x=5\), so the intercept is \((5,0)\). Option \((0,-15)\) is the y-intercept (when \(x=0\), \(p(0)=-15\)), not the x-intercept. Options \((3,0)\) and \((-5,0)\) are simple arithmetic/sign errors — \((3,0)\) would arise from an incorrect solution and \((-5,0)\) flips the sign. Exam tip: for a linear polynomial \(ax+b\), the x-intercept is \((-b/a,0)\).
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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