Question

Determine whether the given values are the solutions of the given equation or not.

$x^2-7x+12=0:x=3,x=4$

• A. Only $x=3$ is a solution of the equation.
• B. Only $x=4$ is a solution of the equation
• C. Both $x=3,4$ are solutions of the equation
• D. None of these

Answer 1

The correct option is C Both $x=3,4$ are solutions of the equation

Let $f\left(x\right)=x^2-7x+12=0$ be the quadratic equation
Now $x=3.x=4$ are the solutions, if $f\left(3\right)=0,f\left(4\right)=0$
Therefore, $f\left(3\right)=3^2-7\left(3\right)+12$
$=9-21+12$
$=0$ and
and $f\left(4\right)=4^2-7\left(4\right)+12$
$=16-28+12$
$=0$
Therefore $x=3,x=4$ are the solutions of the given equation.