If one zero of the polynomial \(p(x)=x^2-10x+r\) is \(4\), what is its other zero?
Answer and explanation
Correct answer: 6
For a quadratic polynomial \(ax^2+bx+c\), the sum of its zeroes is \(-\frac{b}{a}\). Here, the sum is \(-\frac{-10}{1}=10\). Therefore, if one zero is \(4\), the other zero is \(10-4=6\). The value \(4\) is only the given zero, not the other one. Exam tip: use the sum-of-zeroes formula directly when one zero is known.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For a quadratic polynomial \(ax^2+bx+c\), the sum of its zeroes is \(-\frac{b}{a}\). Here, the sum is \(-\frac{-10}{1}=10\). Therefore, if one zero is \(4\), the other zero is \(10-4=6\). The value \(4\) is only the given zero, not the other one. Exam tip: use the sum-of-zeroes formula directly when one zero is known.
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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