Question

Find k for which eq. Has real and equal roots5x2+kx+k=0

Answer 1

Step-by-step explanation:

$5 {x }^{2} + kx + k = 0 \\ equatig \: the \: above \: equation \: with : \\ a{x }^{2} + bx + c = 0 \: we \: find : \\ a = 5 \\ b = k \\ c = k \\ \because \: given \: equation \: has \: real \: and \: \\ equal \: roots. \\ \therefore \: {b}^{2} - 4ac = 0 \\ \therefore \: {k}^{2} - 4 \times 5 \times k = 0 \\ \therefore \: {k}^{2} - 20 k = 0 \\ \therefore \: k( {k} - 20 )= 0 \\ \therefore \: k = 0 \: or \: k - 20 = 0 \\ \therefore \: k = 0 \: or \: k = 20 \\ thus \: k = 0, \: 20$