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:
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:
Show Hint
Vieta's relations allow us to easily find relationships between the roots of quadratic equations.
Updated On: Jan 6, 2026
- \( c \)
- \( d - c \)
- \( 2d \)
- \( 2c \)
Show Solution
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The Correct Option is B
Solution and Explanation
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: \[ \boxed{d - c} \]
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: \[ \boxed{d - c} \]
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