If the roots of the equation \(x^2+px+q=0\) are \(-3\) and \(-4\), what is the value of \(p+q\)?
Answer and explanation
Correct answer: 19
By Vieta’s formulas, the sum of the roots is \(-p\) and their product is \(q\). Thus, \((-3)+(-4)=-7=-p\), giving \(p=7\). Also, \(q=(-3)(-4)=12\). Therefore, \(p+q=7+12=19\). Option 12 is only the value of \(q\). Exam tip: For \(x^2+px+q\), the sum of roots is \(-p\), while their product is \(q\).
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
By Vieta’s formulas, the sum of the roots is \(-p\) and their product is \(q\). Thus, \((-3)+(-4)=-7=-p\), giving \(p=7\). Also, \(q=(-3)(-4)=12\). Therefore, \(p+q=7+12=19\). Option 12 is only the value of \(q\). Exam tip: For \(x^2+px+q\), the sum of roots is \(-p\), while their product is \(q\).
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.
