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

8k-k2=42,
please help

User Rellampec
by
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1 Answer

4 votes

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).


User Simon Bridge
by
6.7k points