Question

Find the values or range of value of P (b) x2 + (2x + 3)x = p has two real and different

Answer 1

Answer:

$The \: given \: quadratic \\ equation \: is, \\ 2 {x}^{2} +3x−p=0 \\ Here, \\a=2, b=3, c=−p \\ If \: the \: equation \: is \: supposed \\ to \: have \: real \: roots, \\ then \: D≥0. \: Therefore, \\ {b}^{2} −4ac≥0 \\ 9−4×2×(−p)≥0 \\ 9+8p≥0 \\ p≤ \frac{9}{8} \\ Thus, \: the \: values \\ of \: p \: for \: which \: the \\ equation \: has \: real \: roots \\ are \: (−∞, \frac{9}{8} ].$