Question

07 Find the values of'k so that the equation (k + 4)x+ (k + 1)x + 1 = 0 has equal roots​

Answer 1

Answer:

(⌒o⌒)(⌒o⌒)(⌒o⌒)(⌒o⌒)(⌒o⌒)(⌒o⌒)(⌒o⌒)(⌒o⌒)(⌒o⌒)(~_^)(~_^)(~_^)(~_^)(~_^)(~_^)(~_^)

$\huge\mathfrak{\underline{\underline{\red{Answer:-}}}}$

$\bigstar \displaystyle \boxed{ \tt{to \: find \: the \: value \: of \: k}}$

$\red \bigstar \displaystyle \tt{equation = (k + 4)x^{2} + (k + 1)x + 1 = 0}$

$\purple \bigstar \displaystyle \tt{by \: using \: determinant \: form}$

$\pink \bigstar \displaystyle \tt{ {b}^{2} - 4ac = 0........(if \: the \: roots \: are \: equal \: }$

$\pink \bigstar \displaystyle \tt{ {(k + 1)}^{2} - 4(k + 4)(1) = 0}$

$\pink \bigstar \displaystyle \tt{ {k}^{2} + 2k + 1 - 4k - 16 = 0}$

$\pink \bigstar \displaystyle \tt{ {k}^{2} - 2k - 15 = 0}$

$\implies \small \boxed{ \sf \pink{by \: factorize}}$

$\pink \bigstar \displaystyle \tt{ {k}^{2} - 5k + 3k - 15 = 0}$

$\pink \bigstar \displaystyle \boxed{\tt \red {k = 5 \: and \: k = - 3}}$