MHT CET · Maths · Quadratic Equation
If the A.M. and G.M. of the roots of a quadratic equation in \(x\) are \(\mathrm{p}\) and q respectively, then its equation is
- A \(x^{2}+2 p x+q^{2}=0\)
- B \(x^{2}+p x+q^{2}=0\)
- C \(x^{2}-p x+q^{2}=0\)
- D \(x^{2}-2 p x+q^{2}=0\)
Answer & Solution
Correct Answer
(D) \(x^{2}-2 p x+q^{2}=0\)
Step-by-step Solution
Detailed explanation
\(v^{\prime}=2 v\)
\(\frac{x_{1}+x_{2}}{2}=p \quad \& \quad \sqrt{x_{1} x_{2}}=q\)
None \(a x^{2}+b x+c=0\)
\(b=-\left(x_{1}+x_{2}\right)\)
\(c=x_{1} x_{2}\)
\(b=-2 p\)
\(\therefore r q^{n}=x^{2}-2 p x+q^{2}=0\)
\(\frac{x_{1}+x_{2}}{2}=p \quad \& \quad \sqrt{x_{1} x_{2}}=q\)
None \(a x^{2}+b x+c=0\)
\(b=-\left(x_{1}+x_{2}\right)\)
\(c=x_{1} x_{2}\)
\(b=-2 p\)
\(\therefore r q^{n}=x^{2}-2 p x+q^{2}=0\)
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