Question

10. Find the least positive value of k for which the equation 2 + x + 4 = 0 has real Roots.​

Answer 1

$The \: given \: equation \: is \\x^2+kx+4=0x2+kx+4=0 \\ A \: quadratic \: equation  \:ax^2+bx+c=0ax2+bx+c=0 has \: real \: roots \: if \\b^2-4ac\geq 0b2−4ac≥0 \\k^2-4(1)(4)\geq 0k2−4(1)(4)≥0 \\k^2-16\geq 0k2−16≥0 \\k^2\geq 16k2≥16 \\ k\geq 4k≥4 \\ The \: value \: of \: k \: must \: be \: greater \: than \: 4, \: therefore \: the   \: least \: value \: of \: k \: is \: 4.$