CBSE Class 10 Maths (Standard) 2017 · Paper 30/1 · Question 11

Quadratic Equations 3 marks Medium

a d \neq = b c

, then prove that the equation

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

has no real roots.

Answer

The discriminant is

D = - 4 (a d - b c)^{2}

, which is

< 0

because

a d \neq = b c

; hence the equation has no real roots.

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