Question

For what value of k are the roots of the quadratic equation(k+4)x*2+(k+1)x+1=0 equal?

Answer 1

roots are equal if d=0
here a= k+4, b= k+1, c = 1
using formula
$d = {b}^{2} - 4ac = 0\\ {(k + 1)}^{2} - 4 \times (k + 4) \times 1 = 0 \\ {k}^{2} + 2k + 1 - 4k - 16 = 0 \\ {k}^{2} - 2k - 15 = 0 \\ (k - 5)(k + 3) = 0 \\ either \: k - 5 = 0 \: or \: k + 3 = 0 \\ k = 5 \: or \: k = - 3$