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If \(p(x)=x^2-5x+6\), what is the value of \(p(2)+p(3)\)?
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Answer and explanation
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The polynomial \(p(x)=x^2-5x+6=(x-2)(x-3)\). Therefore, \(p(2)=0\) and \(p(3)=0\), since 2 and 3 are its zeroes. Hence, \(p(2)+p(3)=0+0=0\). Exam tip: If a number is a zero of a polynomial, the value of the polynomial at that number is directly 0.
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What is the correct answer to this question?
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Why is this the correct answer?
The polynomial \(p(x)=x^2-5x+6=(x-2)(x-3)\). Therefore, \(p(2)=0\) and \(p(3)=0\), since 2 and 3 are its zeroes. Hence, \(p(2)+p(3)=0+0=0\). Exam tip: If a number is a zero of a polynomial, the value of the polynomial at that number is directly 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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