If the two roots of the equation \(x^2+kx+36=0\) are equal and negative, what is the value of \(k\)?
Answer and explanation
Correct answer: 12
The product of the equal roots is \(36\), so each root must be \(-6\), since \((-6)(-6)=36\). Their sum is therefore \(-12\). By Vieta’s formula, the sum of the roots is \(-k\), so \(-k=-12\), giving \(k=12\). Exam tip: You can also use the equal-root condition \(k^2-144=0\); the requirement that the roots be negative selects \(k=12\), not \(-12\).
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The product of the equal roots is \(36\), so each root must be \(-6\), since \((-6)(-6)=36\). Their sum is therefore \(-12\). By Vieta’s formula, the sum of the roots is \(-k\), so \(-k=-12\), giving \(k=12\). Exam tip: You can also use the equal-root condition \(k^2-144=0\); the requirement that the roots be negative selects \(k=12\), not \(-12\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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