If \(p(x)=x^3-4x\), at which x-values does its graph meet the x-axis?
Answer and explanation
Correct answer: -2, 0, 2
Factorize: \(x^3-4x = x(x^2-4)=x(x-2)(x+2)\). The x-intercepts (zeros) are values making any factor zero, so \(x=-2,0,2\). Distractor B is wrong because 4 is not a root (\(4^3-4\cdot4=64-16=48\neq0\)). Exam tip: always factor out the common factor \(x\) first, then factor the remaining quadratic as a difference of squares.
Frequently asked questions
What is the correct answer to this question?
-2, 0, 2
Why is this the correct answer?
Factorize: \(x^3-4x = x(x^2-4)=x(x-2)(x+2)\). The x-intercepts (zeros) are values making any factor zero, so \(x=-2,0,2\). Distractor B is wrong because 4 is not a root (\(4^3-4\cdot4=64-16=48\neq0\)). Exam tip: always factor out the common factor \(x\) first, then factor the remaining quadratic as a difference of squares.
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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