Question: If the roots of the equation $\left( p ^ { 2 } + q ^ { 2 } \right) x ^ { 2 }$ \(a^{2} + c^{2} = - ...

Question

If the roots of the equation $\left( p ^ { 2 } + q ^ { 2 } \right) x ^ { 2 }$ $a^{2} + c^{2} = - ab$ + $a^{2} - c^{2} = - ab$ be real and equal, then $a^{2} - c^{2} = ab$ will be in.

Answer 1

Solution

Given equation is

$ad + bc = 0$

Roots are real and equal, then

$\frac{a}{b} = \frac{c}{d}$

⇒ $x^{2} - 2(1 + 3k)x +$

⇒ $7(3 + 2k) = 0$

⇒ $1, - \frac{10}{9}$ ⇒ $2, - \frac{10}{9}$

Hence $3, - \frac{10}{9}$ . Thus p, q, r in G.P.

Question: If the roots of the equation \(\left( p ^ { 2 } + q ^ { 2 } \right) x ^ { 2 }\) \(a^{2} + c^{2} = - ...

Solution