Question

If the roots of the quadratic equation $$ (a^2 + b^2) \, x^2 - 2 \, (bc + ad) \, x + (c^2 + d^2) = 0 $$ are equal, then: 

• A. \( \frac{a}{b} = \frac{c}{d} \)
• B. \( \frac{a}{c} + \frac{b}{d} = 0 \)
• C. \( \frac{a}{d} = \frac{b}{c} \)
• D. \( a + b = c + d \)

Hint:

For a quadratic equation \( Ax^2 + Bx + C = 0 \), the condition for equal roots is that the discriminant \( D = B^2 - 4AC = 0 \). Use this property to establish relationships between the coefficients.