# Math Help - Real Roots

1. ## Real Roots

show that if k is any real number, the equation x^2 + (k+1)x + k = 0 always has real roots. For what value of k are the roots equal?

2. Originally Posted by casey_k
show that if k is any real number, the equation x^2 + (k+1)x + k = 0 always has real roots. For what value of k are the roots equal?
$\text{descriminant} = {b^2 - 4ac}$

$= {(k+1)^2 - 4(a)(k)}$

$={k^2+2k+1 - 4k}$

$= {k^2-2k+1}$

For these to be real

$k^2 - 2k + 1 \geq 0$

$(k-1)^2 \geq 0$

Is this true for all real numbers ?

For these to be EQUAL

$k^2 - 2k + 1 = 0$

$(k-1)^2 = 0$

$k-1 = 0$

$k = 1$