If the two roots of the quadratic equation \(x^2+bx+49=0\) are equal and each root is \(-7\), what is the value of \(b\)?
Answer and explanation
Correct answer: 14
The sum of the roots is \((-7)+(-7)=-14\). For a quadratic equation \(x^2+bx+c=0\), the sum of the roots is \(-b\). Thus, \(-b=-14\), giving \(b=14\). Option B is the sum of the roots, not the value of the coefficient \(b\). Exam tip: Use the relation \(\text{sum of roots}=-\frac{\text{coefficient of }x}{\text{coefficient of }x^2}\).
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The sum of the roots is \((-7)+(-7)=-14\). For a quadratic equation \(x^2+bx+c=0\), the sum of the roots is \(-b\). Thus, \(-b=-14\), giving \(b=14\). Option B is the sum of the roots, not the value of the coefficient \(b\). Exam tip: Use the relation \(\text{sum of roots}=-\frac{\text{coefficient of }x}{\text{coefficient of }x^2}\).
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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