Question

Find the value of $k$ for which the equation $3x^2-6x+k=0$ has distinct and real root.

Answer 1

$3x^2-6x+k=0$

$Forrealdistinctroots$

$D\ge 0$

$b^2-4ac\ge 0$

${\left(-6\right)}^2-4\times 3\times k\ge 0$

$36-12k\ge 0$

$36\ge 12k$

$k\le 3$