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AP EAMCET · Maths · Quadratic Equation

If the difference of the roots of the equation \(x^2-7 x+10=0\) is same as the difference of the roots of the equation \(\mathrm{x}^2-17 \mathrm{x}+\mathrm{k}=0\), then a divisor of k is

  1. A \(14\)
  2. B \(17\)
  3. C \(6\)
  4. D \(15\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(14\)

Step-by-step Solution

Detailed explanation

\(x^2-7 x+10=0\) \(|\alpha - \beta| = \sqrt{(-7)^2 - 4(10)}\) \(|\alpha - \beta| = \sqrt{49 - 40} = \sqrt{9} = 3\) \(x^2-17 x+k=0\) \(|\gamma - \delta| = \sqrt{(-17)^2 - 4(k)}\) \(3 = \sqrt{289 - 4k}\) \(9 = 289 - 4k\) \(4k = 280\) \(k = 70\) Divisor of \(k\): \(14\)