Question

Please explain who would i be able to get the answer to this problem.

Answer 1

We have been an quadratic equation $8k-k^{2} =42$ and we are asked to solve our equation.

Upon subtracting 42 from both sides of our equation we will get,

$8k-k^{2}-42 =0$

$-k^{2}+8k-42 =0$

$k^{2}-8k+42 =0$

Let us check whether our quadratic equation has any real roots using discriminant formula.

$D=b^{2}-4ac$  

Upon substituting our given values in discriminant formula we will get,

$D=(-8)^{2} -4(1\cdot 42)$

$D=64 -168$

$D=-104$

We can see that D is less than zero, so our quadratic equation has no real roots.

Now we will use imaginary number i to find complex roots of our quadratic equation.

We will use $-1 =i^{2}$ to solve our equation.

$k=\frac{-b \pm \sqrt{b^{2}-4ac} } {2a}$

$k=\frac{--8 \pm \sqrt{(-8)^{2}-4(1*42)} } {2*1}$

$k=\frac{8 \pm \sqrt{64-168 }} {2}$

$k=\frac{8 \pm \sqrt{-1\cdot 104} } {2}$

$k=\frac{8 \pm \sqrt{i^{2}\cdot 104} } {2}$

$k=\frac{8\pm 2i \sqrt{26}}{2}$

$k=4\pm i \sqrt{26}$

Therefore, our answer will be $k=4\pm i \sqrt{26}$.