If 1 is added to each root of the equation \(x^2-6x-16=0\), which monic equation is formed from the resulting roots?
Answer and explanation
Correct answer: \(x^2-8x-9=0\)
The given equation factors as \(x^2-6x-16=(x-8)(x+2)\), so its roots are 8 and −2. Adding 1 to each root gives 9 and −1. Their sum is 8 and their product is −9; therefore, the required monic equation is \(x^2-8x-9=0\). Option B retains the old roots, while option C uses an incorrect sum of the new roots. Exam tip: for roots \(\alpha\) and \(\beta\), form the monic equation as \(x^2-(\alpha+\beta)x+\alpha\beta=0\).
Frequently asked questions
What is the correct answer to this question?
\(x^2-8x-9=0\)
Why is this the correct answer?
The given equation factors as \(x^2-6x-16=(x-8)(x+2)\), so its roots are 8 and −2. Adding 1 to each root gives 9 and −1. Their sum is 8 and their product is −9; therefore, the required monic equation is \(x^2-8x-9=0\). Option B retains the old roots, while option C uses an incorrect sum of the new roots. Exam tip: for roots \(\alpha\) and \(\beta\), form the monic equation as \(x^2-(\alpha+\beta)x+\alpha\beta=0\).
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.
