How to use the discriminant to find out what type of solutions the equation has for $4x^2 + 1 = 0$ ?

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Answer 1 · 2015-05-25T17:22:38

Written in the standard form for a quadratic $ax^2+bx+c=0$

$4x^2 + 1 = 0$
becomes
$4x^2 +(0)x +1 = 0$

The discriminant $Delta = b^2 - 4ac$
becomes
$Delta = -16$

$Delta { (<0 rarr "no Real roots (onlt Complex roots)"), (=0 rarr "1 Real root"),(>0 rarr "2 Real roots"):}$

Therefore
$4x^2+1 = 0$ has only Complex roots

How to use the discriminant to find out what type of solutions the equation has for 4x^2 + 1 = 04x^2 + 1 = 0?