If the roots of \\(x^2+bx+c=0\\) are \\(-2\\) and \\(7\\), what is the value of \\(b+c\\)?
Answer and explanation
Correct answer: -19
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 \\(-2+7=5\\), so \\(-b=5\\), giving \\(b=-5\\). The product is \\((-2)\\times7=-14\\), so \\(c=-14\\). Therefore, \\(b+c=-5-14=-19\\). Exam tip: For \\(ax^2+bx+c=0\\), use the root sum \\(-b/a\\) and root product \\(c/a\\).
Frequently asked questions
What is the correct answer to this question?
-19
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 \\(-2+7=5\\), so \\(-b=5\\), giving \\(b=-5\\). The product is \\((-2)\\times7=-14\\), so \\(c=-14\\). Therefore, \\(b+c=-5-14=-19\\). Exam tip: For \\(ax^2+bx+c=0\\), use the root sum \\(-b/a\\) and root product \\(c/a\\).
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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