SOLUTION: Consider the quadratic equation x^2 + 4x + c = 0. For what range of values of c does the equation have two real roots? Hint: the answer is an inequality.

SOLUTION: Consider the quadratic equation x^2 + 4x + c = 0. For what range of values of c does the equation have two real roots? Hint: the answer is an inequality.

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Question 796785: Consider the quadratic equation x^2 + 4x + c = 0.
For what range of values of c does the equation have two real roots? Hint: the answer is an inequality.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I presume you mean two different real roots.

For the general quadratic equation,

,

if

, then there are two real roots,

and

such that

.

if

, then there are two real roots,

and

such that

. Note: The modern way of saying this is that there is one root with a multiplicity of two mostly because students can't seem to get their heads around the idea that two roots is two roots even if they are identical because the quadratic has two real number factors. They just happen to be the same factors because this is the perfect square case.

and if

, then there is a conjugate pair of complex roots,

and

of the form

where

is the imaginary number defined by

.

So, in order to have two different real roots, you must have

strictly greater than

where

and

John

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