Question
Download Solution PDFIf the roots of the equation 4x2 - (5k + 1)x + 5k = 0 differ by unity, then which one of the following is a possible value of k?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
Quadratic equation: ax2 + bx + c = 0
let the two roots be r1 and r2
Sum of the roots: r1 + r2 =
Calculation:
let the roots of the equation 4x2 - (5k + 1)x + 5k = 0 be α and α + 1
α + α + 1 =
⇒ α =
⇒ α (α + 1) =
⇒
⇒ (5k − 3)(5k + 5) = 80k
⇒ (5k − 3)(k + 1) = 16k
⇒ 5k2 − 14k − 3 = 0
⇒ (k − 3)(5k + 1) = 0
⇒ k = 3,
∴ One of the possible value is -1/5.
Last updated on May 30, 2025
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