Question

please answer it guys
I need it urgently ​

Answer 1

Step-by-step explanation:

The given quadratic equation is $x^{2}+2(m-1)x+(m+5)=0$

Since, its roots are real and equal, so,

its discriminant will be zero.

So,

$\{ 2(m - 1)\}^{2} - 4.(1).(m + 5) = 0$

$\implies 4(m - 1)^{2} - 4(m + 5) = 0$

$\implies 4 \{(m - 1)^{2} -(m + 5) \} = 0$

$\implies (m - 1)^{2} -m - 5 = 0$

$\implies (m)^{2} - 2.(1).(m) + (1)^{2} -m - 5 = 0$

$\implies m^{2} - 2m + 1 -m - 5 = 0$

$\implies m^{2} -3m - 4 = 0$

$\implies m^{2} -4m + m - 4 = 0$

$\implies m(m -4) +1( m - 4) = 0$

$\implies (m + 1)(m -4) = 0$

$\implies m = - 1 \: \: or \: \: m = 4$