If the roots of the quadratic equation \(x^2+bx+c=0\) are \(-5\) and \(11\), what is the value of \(b+c\)?
Answer and explanation
Correct answer: -61
For the quadratic equation \(x^2+bx+c=0\), the sum of the roots is \(-b\) and their product is \(c\). Here, the sum is \(-5+11=6\), so \(-b=6\), giving \(b=-6\). Their product is \((-5)(11)=-55\), so \(c=-55\). Therefore, \(b+c=-6-55=-61\). Exam tip: In a monic quadratic, use the root relations sum \(=-b\) and product \(=c\) directly.
Frequently asked questions
What is the correct answer to this question?
-61
Why is this the correct answer?
For the quadratic equation \(x^2+bx+c=0\), the sum of the roots is \(-b\) and their product is \(c\). Here, the sum is \(-5+11=6\), so \(-b=6\), giving \(b=-6\). Their product is \((-5)(11)=-55\), so \(c=-55\). Therefore, \(b+c=-6-55=-61\). Exam tip: In a monic quadratic, use the root relations sum \(=-b\) and product \(=c\) directly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
