If the roots of the quadratic equation \(x^2+bx+c=0\) are \(-3\) and \(8\), what is the value of \(b+c\)?
Answer and explanation
Correct answer: -29
For the monic quadratic equation \(x^2+bx+c=0\), the sum of the roots is \(-b\) and their product is \(c\). Here, the sum is \(-3+8=5\), so \(-b=5\), giving \(b=-5\). The product is \((-3)(8)=-24\), so \(c=-24\). Therefore, \(b+c=-5-24=-29\). Exam tip: For \(x^2+bx+c=0\), use \(b=-(\text{sum of roots})\) and \(c=\text{product of roots}\).
Frequently asked questions
What is the correct answer to this question?
-29
Why is this the correct answer?
For the monic quadratic equation \(x^2+bx+c=0\), the sum of the roots is \(-b\) and their product is \(c\). Here, the sum is \(-3+8=5\), so \(-b=5\), giving \(b=-5\). The product is \((-3)(8)=-24\), so \(c=-24\). Therefore, \(b+c=-5-24=-29\). Exam tip: For \(x^2+bx+c=0\), use \(b=-(\text{sum of roots})\) and \(c=\text{product of roots}\).
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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