How do you find the value of the discriminant and state the type of solutions given $4k^2+5k+4=-3k$ ?

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Answer 1 · 2017-10-20T19:46:08

$Delta = 0$
$1$ repeated root

rearrange the equation into the form $ak^2+bk+c=0$ :

$4k^2+5k+4=-3k$
$4k^2+5k+3k+4=0$
$4k^2+8k+4=0$

divide both sides by $4$ :
$k^2+2k+1=0$

$ak^2+bk+c=0$
$k^2+2k+1=0$

$therefore a=1, b=2, c=1$

$Delta$ (discriminant) $= (b^2-4ac)$ for a quadratic equation

here, $b^2-4ac = 2^2-(4*1*1)$
$=4-4$
$=0$

$0=0$
since $Delta=0, k$ has $1$ repeated root.

on a graph:
![https://www.desmos.com/calculator]( useruploads.socratic.org )

the parabola only meets the $x$ -axis once- there is only $1$ root.

through factorisation:

$k^2+2k+1=0$
$(k+1)(k+1)=0$
solving for $k$ , you get
' $k = -1$ or $k=-1$ '

the number $-1$ is repeated, giving the name 'repeated root'.

How do you find the value of the discriminant and state the type of solutions given 4k^2+5k+4=-3k4k^2+5k+4=-3k?