Question: If the roots of $\left( a^{2} + b^{2} \right)x^{2} - 2b(a + c)x + (b^{2} + c^{2}) = 0$ are equal t...

Question

If the roots of $\left( a^{2} + b^{2} \right)x^{2} - 2b(a + c)x + (b^{2} + c^{2}) = 0$ are equal then a, b, c are in

Answer 1

(a² + b²) x² – 2b (a + c) x + b² + c² = 0

 a²x² – 2bax + b² + b²x² –2bcx + c² = 0

 (ax – b)² +(bx – c)² a = 0

 ax – b = 0 and bx – c =0

 $x = \frac{b}{a}$ and $x = \frac{c}{b}$

 $\frac{b}{a} = \frac{c}{b}$  a, b, c are in G.P.

Question: If the roots of \(\left( a^{2} + b^{2} \right)x^{2} - 2b(a + c)x + (b^{2} + c^{2}) = 0\) are equal t...