WBJEE · Maths · Quadratic Equation
If \(p, q\) are odd integers, then the roots of the equation \(2 p x^{2}+(2 p+q) x+q=0\) are
- A rational
- B irrational
- C non-real
- D equal
Answer & Solution
Correct Answer
(A) rational
Step-by-step Solution
Detailed explanation
Given equation. \[ \begin{array}{l} 2 p x^{2}+(2 p+q) x+q=0 \\ \therefore D=(2 p+q)^{2}-4(2 p)(q) \\ \quad=4 p^{2}+q^{2}+4 p q-8 p q \\ \quad=4 p^{2}+q^{2}-4 p q \\ \quad=(2 p-q)^{2} \end{array} \] \(=\) a perfect square Given equation has rational roots
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