Question

For what value of k are roots quqdrqtic equation :(k-4)xsquare(k-4)x+4=0equals.

Answer 1

for roots being equal D = 0
$d = {b}^{2} - 4ac = 0 \\( {k - 4)}^{2} - 4(4)(k -4 ) = 0 \\ {k}^{2} - 8k + 16 - 16k + 64 = 0 \\ {k}^{2} - 24k + 80 = 0 \\ {k}^{2} - 20k - 4k + 80 = 0 \\ k(k - 20) - 4(k - 20) = 0 \\ (k - 4)(k - 20) = 0 \\ k - 4 = 0 \\ k = 4 \\ k - 20 = 0 \\ k = 20$