Question

subtract 24 minutes 54 seconds from 36minutes 23seconds​

Answer 1

$\huge\mathcal{\underline{\color{olive}QUESTION}}$

★ Find the value of k such that the equation (2k + 3) x² + 2(k + 3) + (k + 5) = 0 has equal roots .

$\huge{\orange{\boxed{\fcolorbox{lime}{cadetblue}{\purple{ANSWER}}}}}$

$\red\bullet\:\bf{(2k~+~3)~x^2~+~2(k~+~3)~+~(k~+~5)~=~0~}$

Here,

a = (2k + 3)

b = 2(k + 3)

c = (k + 5)

᪥ As we know that,

$\longrightarrow\:\sf{D~=~b^2~-~4ac~}$

$\longrightarrow\:\sf{D~=~\Big\{2(k~+~3~)\Big\}^2~-~4\times(2k~+~3)\times(k~+~5)~}$

$\longrightarrow\:\sf{D~=~4(k^2~+~9~+~6k)~-~4\times(2k^2~+~10k~+~3k~+~15)~}$

$\longrightarrow\:\sf{D~=~4k^2~+~36~+~24k~-~8k^2~-~40k~-~12k~-~60~}$

$\longrightarrow\:\sf{D~=~4k^2~+~36~+~24k~-~8k^2~-~52k~-~60~}$

$\longrightarrow\:\sf{D~=~-~4k^2~-~24~-~28k~}$

$\longrightarrow\:\sf{D~=~-4~(k^2~+~7k~+~6)~}$

☢︎︎ The given equation will have equal roots,

If D = 0 .

╰➝ -4 (k² + 7k + 6) = 0

╰➝ k² + 7k + 6 = 0

╰➝ k² + 6k + k + 6 = 0

╰➝ k (k + 6) + 1 (k + 6) = 0

╰➝ (k + 6) (k + 1) = 0

╰➝ k + 6 = 0 (or) k + 1 = 0

╰➝ k = -6 (or) k = -1

∴ The value of k is “ -6 or -1 ” .

Answer 2

Answer:

11.4833333 Minutes

This is the answer