If the graph of a quadratic polynomial (p(x)) cuts the (x)-axis at (-2) and (5), how many zeroes does it have?
Answer and explanation
Correct answer: Two
A zero of a polynomial is an x-value at which its graph meets the x-axis, because the y-value there is \(p(x)=0\). The question says that the graph cuts the x-axis at two different positions, \(x=-2\) and \(x=5\). Each position gives one zero, so the quadratic polynomial has two zeroes. These are distinct real zeroes because the two x-values are different.
This can also be understood from the factor form: a quadratic with these zeroes would be proportional to \((x+2)(x-5)\). The two factors become zero at \(-2\) and \(5\), respectively. Therefore the number of zeroes is two, and option A is correct. The answer is not one, because the graph has two separate x-intercepts; it is not three, because a quadratic polynomial can have at most two zeroes. “No zeroes” would apply only if the graph did not meet the x-axis.
Frequently asked questions
What is the correct answer to this question?
Two
Why is this the correct answer?
A zero of a polynomial is an x-value at which its graph meets the x-axis, because the y-value there is \(p(x)=0\). The question says that the graph cuts the x-axis at two different positions, \(x=-2\) and \(x=5\). Each position gives one zero, so the quadratic polynomial has two zeroes. These are distinct real zeroes because the two x-values are different.
This can also be understood from the factor form: a quadratic with these zeroes would be proportional to \((x+2)(x-5)\). The two factors become zero at \(-2\) and \(5\), respectively. Therefore the number of zeroes is two, and option A is correct. The answer is not one, because the graph has two separate x-intercepts; it is not three, because a quadratic polynomial can have at most two zeroes. “No zeroes” would apply only if the graph did not meet the x-axis.
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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