CBSE Class 10 Maths (Standard) 2017 · Paper 30/3 · Question 20

Quadratic Equations 3 marks Medium

If the roots of the equation

(a^{2} + b^{2}) x^{2} - 2 (a c + b d) x + (c^{2} + d^{2}) = 0

are equal, prove that

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

Answer

The equal-roots condition forces the discriminant to zero, giving

(a d - b c)^{2} = 0

, so

a d = b c

and hence

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

🔒 Step-by-step solution

Class 10 Maths — every question with an expert-verified, step-by-step solution.