Question

If the equation (m-1)x2 + 2(m-3)X + (2m-3) = 0 have equal roots, then the value of m can be

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The equation}$

$\mathsf{(m-1)x^2+2(m-3)x+(2m-3)=0\;has\;equal\;roots}$

$\underline{\textbf{To find:}}$

$\textsf{The value of m}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider}$

$\mathsf{(m-1)x^2+2(m-3)x+(2m-3)=0}$

$\mathsf{Here,\;a=m-1,\;b=2(m-3),\;c=2m-3}$

$\textsf{Since the given equation has equal roots,}$

$\mathsf{we\;have\;b^2-4ac=0}$

$\implies\mathsf{[2(m-3)]^2-4(m-1)(2m-3)=0}$

$\implies\mathsf{4(m-3)^2-4(m-1)(2m-3)=0}$

$\implies\mathsf{4(m^2+9-6m)-4(2m^2-3m-2m+3)=0}$

$\implies\mathsf{(m^2+9-6m)-(2m^2-5m+3)=0}$

$\implies\mathsf{m^2+9-6m-2m^2+5m-3=0}$

$\implies\mathsf{-m^2-m+6=0}$

$\implies\mathsf{m^2+m-6=0}$

$\textsf{Factorizing we get}$

$\mathsf{(m+3)(m-2)=0}$

$\implies\mathsf{m=-3,2}$

$\underline{\textbf{Answer:}}$

$\textbf{The values of m are -3 and 2}$