If the graph of a polynomial passes through the points \((-4,0), (0,3), (2,0)\) and \((5,-1)\), which are its real zeroes?
Answer and explanation
Correct answer: -4 and 2
Real zeros of a polynomial are the x-values where the graph meets the x-axis, i.e. where \(y=0\). Among the given points only \((-4,0)\) and \((2,0)\) have \(y=0\), so the zeros are \(-4\) and \(2\). Closest distractor B is wrong because \((0,3)\) has \(y=3\) and \((5,-1)\) has \(y=-1\); neither lies on the x-axis. Exam tip: pick x-coordinates only from points whose y-coordinate equals zero.
Frequently asked questions
What is the correct answer to this question?
-4 and 2
Why is this the correct answer?
Real zeros of a polynomial are the x-values where the graph meets the x-axis, i.e. where \(y=0\). Among the given points only \((-4,0)\) and \((2,0)\) have \(y=0\), so the zeros are \(-4\) and \(2\). Closest distractor B is wrong because \((0,3)\) has \(y=3\) and \((5,-1)\) has \(y=-1\); neither lies on the x-axis. Exam tip: pick x-coordinates only from points whose y-coordinate equals zero.
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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