Question

If x₁ and x₂ are the arithmetic and harmonic mean of the roots of the equations ax² + bx + c = 0, then quadratic equation whose roots are x₁ and x₂ is

• A. abx² + (b² + ac)x + bc = 0
• B. 2ab x² + (b² + 4ac)x + 2bc = 0
• C. 2abx² + (b² + ac)x + bc = 0
• D. None of these

Answer 1

Answer: (B)

2ab x² + (b² + 4ac)x + 2bc = 0

Answer 2

a + b = – $\frac{b}{a}$, ab = $\frac{c}{a}$

x² – x $\left( \frac{\alpha + \beta}{2} + \frac{2\alpha\beta}{\alpha + \beta} \right)$ + ab = 0

x² + x$\left( \frac{b^{2} + 4ac}{2ab} \right) + \frac{c}{a}$= 0

i.e. 2ab x² + (b² + 4ac) x + 2bc = 0