If the zeros of the polynomial \(x^2+mx+n\) are \(0\) and \(5\), what is the value of \(m+n\)?
Answer and explanation
Correct answer: −5
For the quadratic polynomial \(x^2+mx+n\), the sum of its zeros is \(-m\) and their product is \(n\). Here, the sum is \(0+5=5\), so \(-m=5\), giving \(m=-5\). Their product is \(0\times5=0\), so \(n=0\). Therefore, \(m+n=-5+0=-5\). Exam tip: In the standard form \(x^2+mx+n\), remember that the sum of zeros is \(-m\) and the product is \(n\).
Frequently asked questions
What is the correct answer to this question?
−5
Why is this the correct answer?
For the quadratic polynomial \(x^2+mx+n\), the sum of its zeros is \(-m\) and their product is \(n\). Here, the sum is \(0+5=5\), so \(-m=5\), giving \(m=-5\). Their product is \(0\times5=0\), so \(n=0\). Therefore, \(m+n=-5+0=-5\). Exam tip: In the standard form \(x^2+mx+n\), remember that the sum of zeros is \(-m\) and the product is \(n\).
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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