Question

te value of p for equation 2x2 - 4x + p = 0 to have real roots will be ​

Answer 1

Step-by-step explanation:

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$\\value \: \: of \: \: p ? \\ \\ 2{x}^{2} - 4x + p = 0$

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$\\ \leadsto 2 {x}^{2} - 4x + p = 0 \\ \\ here \\ \\ if \: \: roots \: \: are \: \: real... \\ \\ then \: \: \boxed{ {b}^{2} - 4ac \geq 0} \\ \\ \implies {b}^{2} - 4ac \geq 0 \\ \\ \implies {( - 4)}^{2} - 4(2)(p) \geq 0 \\ \\ \implies 16 - 8p \geq 0 \\ \\ \implies 8p \leq 16 \\ \\ \huge \boxed{ \implies p \leq 2} \\ \\ If \: \: D = {b}^{2} - 4ac = 0 \: \: then \: \: both \: \: roots \: \: are \\ real \: \: and \: \: equal \\ \\ If \: \: D = {b}^{2} - 4ac > 0 \: \: then \: \: both \: \: roots \: \: are \\ real \: \: and \: \: not \: \: equal \\ \\ If \: \: D = {b}^{2} - 4ac < 0 \: \: then \: \: both \: \: roots \: \: are \\ not \: \: real$