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AP EAMCET2014MathematicsQuadratic Equation

If x₁ and x₂ are the real roots of the equation x^2-k x+c=0 , then the distance between the points A (x₁, 0 ) and B (x₂, 0 ) is

Options

  1. Ak^2+4 c
  2. Bk^2-c
  3. Cc-k^2
  4. Dk^2-4 c

Correct answer

D. k^2-4 c

Step-by-step solution

Given, x₁ and x₂ are the roots of the equation array rlrl & & x^2-p x+c & =0 & and & x₁+x₂ & =k & x₁ x₂ & =-c array The distance between A (x₁, 0 ) and B (x₂, 0 ) is aligned A B & = (x₂-x₁ )^2+0^2 = |x₂-x₁ | & = (x₁+x₂ )^2-4 x₁ x₂ & = k^2-4 1 c & = k^2-4 c aligned

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