Which of the following equations has 2 as a root?

Solution:

(c)

(a) Substitutina $x=2$ in $x^{2}-4 x+5$, we get $(2)^{2}-4(2)+5$

$=4-8+5=1 \neq 0$

So, $x=2$ is not a root of $x^{2}-4 x+5=0$

(b) Substituting $x=2$ in $x^{2}+3 x-12$, we get

$(2)^{2}+3(2)-12$

$=4+6-12=-2 \neq 0$

So, $x=2$ is not a root of $x^{2}+3 x-12=0$.

(c) Substituting $x=2$ in $2 x^{2}-7 x+6$, we get

$2(2)^{2}-7(2)+6=2(4)-14+6$

$=8-14+6=14-14=0$

So, $x=2$ is root of the equation $2 x^{2}-7 x+6=0$

(d) Substituting $x=2$ in $3 x^{2}-6 x-2$, we get

$3(2)^{2}-6(2)-2$

$=12-12-2=-2 \neq 0$

So, $x=2$ is not a root of $3 x^{2}-6 x-2=0$