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Discuss the nature of roots of equation ...

Discuss the nature of roots of equation ` x^(2) +ax +b =0 and x^(2) +cx + d=0, where a,b,c, d are real numbers and `ac = 2( b +d)`

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To discuss the nature of the roots of the equations \( x^2 + ax + b = 0 \) and \( x^2 + cx + d = 0 \) given the condition \( ac = 2(b + d) \), we will analyze the discriminants of both quadratic equations. ### Step 1: Identify the discriminants For a quadratic equation of the form \( x^2 + px + q = 0 \), the discriminant \( D \) is given by: \[ D = p^2 - 4q \] Thus, for the first equation \( x^2 + ax + b = 0 \): ...
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