Equal roots condition (find P): For 3x^2 − 5x + P = 0, determine the value(s) of P for which the equation has equal (repeated) real roots.
Aptitude
Quadratic Equation
Difficulty: Easy
Choose an option
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A−25/12
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B25/6
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C25/12
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D−25/6
Answer
Correct Answer: 25/12
Explanation
Introduction / Context:A quadratic has equal real roots exactly when its discriminant is zero. We compute the discriminant for 3x^2 − 5x + P and set it to zero to find P.Given Data / Assumptions:
- a = 3, b = −5, c = P.
Concept / Approach:Δ = b^2 − 4ac = (−5)^2 − 4*3*P. Set Δ = 0 and solve for P.Step-by-Step Solution:
Δ = 25 − 12P.Set Δ = 0 ⇒ 25 − 12P = 0 ⇒ 12P = 25 ⇒ P = 25/12.Verification / Alternative check:With P = 25/12 the quadratic becomes 3x^2 − 5x + 25/12 = 0. Completing the square confirms a repeated root.
Why Other Options Are Wrong:
- −25/12, 25/6, −25/6 give Δ ≠ 0, hence not equal roots.
Common Pitfalls:Arithmetic slips with 4ac or sign errors when b is negative. Always compute Δ carefully.
Final Answer:
25/12