AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(a x^2+a x+c=0\) are in the ratio \(p: q\), then \(\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}=\)
- A \(\sqrt{\frac{a^2}{c}}\)
- B \(\sqrt{\frac{a}{2 c}}\)
- C \(\sqrt{\frac{a}{c}}\)
- D \(\sqrt{\frac{a^2}{2 c}}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{a}{c}}\)
Step-by-step Solution
Detailed explanation
Equation given be, \(\begin{aligned} a x^2+a x+c & =0 \\ \therefore \text { Sum of roots }=-\frac{a}{a} & =-1 \end{aligned}\) \(\therefore\) Sum of roots \(=-\frac{a}{a}=-1\) and product of roots \(=\frac{c}{a}\). Now roots are given in ratio \(\frac{p}{q}\), i.e.,…
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