If both roots of \(x^2+bx+144=0\) are equal and each is \(-12\), what is the value of \(b\)?
Answer and explanation
Correct answer: 24
For a quadratic, the sum of roots is \(\alpha+\beta=-b/a\). Here \(a=1\) and both roots are \(-12\), so the sum is \(-24\). Thus \(-b=-24\) which gives \(b=24\). Alternatively, for a repeated root use \(-b/(2a)\): \(-b/2=-12\) leads to the same result. The distractor \(-24\) is the sign-error mirror of the correct sum, so it is incorrect. Exam tip: use \(\alpha+\beta=-b/a\) and \(\alpha\beta=c/a\) and double-check signs when substituting.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
For a quadratic, the sum of roots is \(\alpha+\beta=-b/a\). Here \(a=1\) and both roots are \(-12\), so the sum is \(-24\). Thus \(-b=-24\) which gives \(b=24\). Alternatively, for a repeated root use \(-b/(2a)\): \(-b/2=-12\) leads to the same result. The distractor \(-24\) is the sign-error mirror of the correct sum, so it is incorrect. Exam tip: use \(\alpha+\beta=-b/a\) and \(\alpha\beta=c/a\) and double-check signs when substituting.
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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