If the roots of \(x^2+ax+10=0\) are \(-2\) and \(-5\), what is the value of \(a\)?
Answer and explanation
Correct answer: 7
Use Vieta's relations. For \(x^2+ax+10=0\), the sum of roots equals \(-a\) and the product equals \(10\). The given roots sum to \(-2)+(-5)=-7\, so \(-a=-7\) and hence \(a=7\). Check the product: \((-2)(-5)=10\) matches the constant term, confirming consistency. The closest distractor \(-7\) stems from reversing the sign convention (thinking sum equals \(a\) instead of \(-a\)). Exam tip: For \(x^2+bx+c=0\) remember sum = \(-b\) and product = \(c\) to avoid sign mistakes.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Use Vieta's relations. For \(x^2+ax+10=0\), the sum of roots equals \(-a\) and the product equals \(10\). The given roots sum to \(-2)+(-5)=-7\, so \(-a=-7\) and hence \(a=7\). Check the product: \((-2)(-5)=10\) matches the constant term, confirming consistency. The closest distractor \(-7\) stems from reversing the sign convention (thinking sum equals \(a\) instead of \(-a\)). Exam tip: For \(x^2+bx+c=0\) remember sum = \(-b\) and product = \(c\) to avoid sign mistakes.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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