If the two roots of the equation \(x^2+kx+49=0\) are equal and negative, what is the value of \(k\)?
Answer and explanation
Correct answer: 14
Let the equal root be \(r\). Since the product of the roots is \(49\), we have \(r^2=49\), giving \(r=\pm7\). Because the roots are negative, \(r=-7\). Thus, their sum is \(-14\). By Vieta’s formula, the sum of the roots is \(-k\), so \(-k=-14\) and \(k=14\). Exam tip: use the constant term to find the equal root first, then use the sum of roots \(-k\) to determine the coefficient.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Let the equal root be \(r\). Since the product of the roots is \(49\), we have \(r^2=49\), giving \(r=\pm7\). Because the roots are negative, \(r=-7\). Thus, their sum is \(-14\). By Vieta’s formula, the sum of the roots is \(-k\), so \(-k=-14\) and \(k=14\). Exam tip: use the constant term to find the equal root first, then use the sum of roots \(-k\) to determine the coefficient.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
