Question

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

8k-k2=42,
please help

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 √(64-168 )} {2}`

`k=\frac{8 \pm √(-1\cdot 104) } {2}`

`k=\frac{8 \pm \sqrt{i^(2)\cdot 104} } {2}`

`k=(8\pm 2i √(26))/(2)`

`k=4\pm i √(26)`

Therefore, our answer will be
`k=4\pm i √(26)`.