If the zeroes of the polynomial \(p(x)=x^2+px+q\) are 4 and −5, what is the value of \(p+q\)?
Answer and explanation
Correct answer: −19
The sum of the zeroes is \(4+(-5)=-1\). For the quadratic polynomial \(x^2+px+q\), the sum of the zeroes is \(-p\), so \(-p=-1\) and hence \(p=1\). Their product is \(4\times(-5)=-20\), giving \(q=-20\). Therefore, \(p+q=1-20=-19\). Exam tip: For \(x^2+px+q\), remember that the sum of zeroes is \(-p\) and their product is \(q\).
Frequently asked questions
What is the correct answer to this question?
−19
Why is this the correct answer?
The sum of the zeroes is \(4+(-5)=-1\). For the quadratic polynomial \(x^2+px+q\), the sum of the zeroes is \(-p\), so \(-p=-1\) and hence \(p=1\). Their product is \(4\times(-5)=-20\), giving \(q=-20\). Therefore, \(p+q=1-20=-19\). Exam tip: For \(x^2+px+q\), remember that the sum of zeroes is \(-p\) and their product is \(q\).
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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