Tianna Mayer

2022-12-31

If one of the roots of the equation ${x}^{2}+kx=6$ is 2, what is the value of k?

mercerizoblx

Expert

${x}^{2}-Sx+P=0⇔{x}^{2}+kx-6=0$
$a+b=-k$
$ab=-6$
$b=2⇒a=-3$
$-3+2=-k$
$-1=-k$

Expert

Let's resolve the quadratic equation for k:
$kx=6-{x}^{2}$
$k=\frac{6-{x}^{2}}{x}$
Let's plug it into the equation and find k if one root equals 2.
$k=\frac{6-\left({2}^{2}\right)}{2}=\frac{6-4}{2}=\frac{2}{2}$
$k=1$

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