AP EAMCET · Maths · Quadratic Equation
The harmonic mean of two numbers is \(-\frac{8}{5}\) and their geometric mean is 2 . The quadratic equation whose roots are twice those numbers is
- A \(x^2+5 x+4=0\)
- B \(x^2+10 x+16=0\)
- C \(x^2-10 x+16=0\)
- D \(x^2-5 x+4=0\)
Answer & Solution
Correct Answer
(B) \(x^2+10 x+16=0\)
Step-by-step Solution
Detailed explanation
Let two numbers be \(a\) and \(b\) G.M. \(=\sqrt{a b}=2\) Now, \(\quad\) H.M. \(=\frac{2 a b}{a+b}=-\frac{8}{5}\) \[ \frac{2 \times 4}{a+b}=-\frac{8}{5} \quad \text { (from Eq. (i)) } \] \[ \therefore \quad a+b=-5 \] Here, roots are twice of these numbers. So,…
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