Question

Let $f\left(x\right)=x^2+x-6$. For what values of $t$ is $f(t-5)=0$?

• A. $-3$ and $2$
• B. $-2$ and $3$
• C. $5$
• D. $2$ and $7$

Answer 1

The correct option is D $2$ and $7$

$Given,f\left(x\right)=x^2+x-6$
Then $f\left(t\right)=t^2+t-6$
Also given $f(t-5)=0$
Then $f(t-5)=(t-5{)}^2+(t-5)+6=0$
$\Rightarrow t^2-10t+25+t-5-6=0$
$\Rightarrow t^2-9t+14=0$
$\Rightarrow t^2-7t-2t+14=0$
$\Rightarrow t(t-7)-2(t-7)=0$
$\Rightarrow (t-2)(t-7)=0$
Then $t=2$ or $t=7$