If both roots of the quadratic equation \\(x^2+bx+64=0\\) are equal and each root is \\(-8\\), what is the value of \\(b\\)?
Answer and explanation
Correct answer: 16
The roots are \\(-8\\) and \\(-8\\), so their sum is \\(-16\\). For \\(x^2+bx+64=0\\), the sum of the roots is \\(-b\\). Therefore, \\(-b=-16\\), giving \\(b=16\\). Option B is the root sum, not the coefficient \\(b\\). Exam tip: In \\(x^2+px+q=0\\), the sum of roots is \\(-p\\) and their product is \\(q\\).
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The roots are \\(-8\\) and \\(-8\\), so their sum is \\(-16\\). For \\(x^2+bx+64=0\\), the sum of the roots is \\(-b\\). Therefore, \\(-b=-16\\), giving \\(b=16\\). Option B is the root sum, not the coefficient \\(b\\). Exam tip: In \\(x^2+px+q=0\\), the sum of roots is \\(-p\\) and their product is \\(q\\).
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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