consider the quadratic function x^2-(k+2)x+4=0
for what value of k does the quadratic function have real roots?
+118723 consider the quadratic function x^2-(k+2)x+4=0
for what value of k does the quadratic function have real roots?
The roots will be reall when the determinant is greater than or equal to 0.
\(\triangle\ge0\\ (k+2)^2-4*1*4\ge0\\ k^2+4k+4-16\ge0\\ k^2+4k-12\ge0\\ (k+6)(k-2)\ge0\\ NOW\;\;consider\\ y=k^2+4k-12\\ \mbox{Since the coefficient of k is positive, this is a concave up parabola}\\ \mbox{So the expression will be greater than zero at the ends.} \mbox{The roots are -6 and 2}\\ \mbox{so the roots will be real when } \;\;k\le-6 \quad and \quad when \quad k\ge 2 \)
