AP EAMCET · Maths · Quadratic Equation
If \(x_1\) and \(x_2\) are the real roots of the equation \(x^2-k x+c=0\), then the distance between the points \(A\left(x_1, 0\right)\) and \(B\left(x_2, 0\right)\) is
- A \(\sqrt{k^2+4 c}\)
- B \(\sqrt{k^2-c}\)
- C \(\sqrt{c-k^2}\)
- D \(\sqrt{k^2-4 c}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{k^2-4 c}\)
Step-by-step Solution
Detailed explanation
Given, \(x_1\) and \(x_2\) are the roots of the equation \[ \begin{array}{rlrl} & \therefore & x^2-p x+c & =0 \\ & \text { and } & x_1+x_2 & =k \\ & x_1 x_2 & =-c \end{array} \] \(\therefore\) The distance between \(A\left(x_1, 0\right)\) and \(B\left(x_2, 0\right)\) is…
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