Question

If the roots of the equation \( x^2 + ax + b = 0 \) are \( c \) and \( d \), then one of the roots of the equation \[ x^2 + (2c + a)x + c^2 + ac + b = 0 \] is:

• A. \( c \)
• B. \( d - c \)
• C. \( 2d \)
• D. \( 2c \)

Hint:

Vieta's relations allow us to easily find relationships between the roots of quadratic equations.

Answer 1

The Correct Option is B

Step 1: Use Vieta's relations.
Vieta’s relations give the sum and product of the roots of a quadratic equation. By substituting \( c \) and \( d \) in the second equation, we can find one of the roots.
Step 2: Conclusion.
After applying Vieta’s formulas, we find that the root is \( d - c \).
Final Answer: \[ \boxed{d - c} \]