AP EAMCET · Maths · Quadratic Equation
For which value of ' \(k\) ', the roots of equation \(2 x^2+5 x+k=0\) are rational?
- A \(\frac{5}{8}\)
- B \(\frac{25}{8}\)
- C \(\frac{25}{4}\)
- D \(\frac{5}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{25}{8}\)
Step-by-step Solution
Detailed explanation
Given, quadratic equation is \[ 2 x^2+5 x+k=0 \] Quadratic equation have rational roots when \(D\) is perfect square, \[ \begin{aligned} & D=b^2-4 a c=25-4 \cdot 2 k \\ & D=25-8 k \end{aligned} \] from options checking \(k=\frac{25}{8}\) makes \(D\) is perfect square…
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