Question

Solve for x in the equation x2-8x+41=0

Answer 1

Choice d is correct answer.

Explanation:

We have given a quadratic equation.

x²-8x+41 = 0

We have to solve above equation using quadratic formula.

x²-8x+41 = 0 is general form of quadratic equation, where a = 1, b = -8 and c = 41.

x = (-b±√b²-4ac) / 2a is quadratic formula.

Putting given values in above equation, we have

x = (-(-8)±√(-8)²-4(1)(41) ) / 2(1)

x = (8±√64-164) / 2

x = (8±√-100) / 2

x = (8±√100√-1) / 2

x = (8 ± 10i) / 2

x = 4±5i which is the solution of given equation.

Answer 2

d) 4 ± 5i

Explanation:

Here we have to use the quadratic formula.

x =
`(-b +/- √(b^2 - 4ac) )/(2a)`

In the given equation x^2 - 8x + 41 = 0, a =1, b = -8 and c = 41

Now plug in the given values in the above formula, we get

x =
`(-(-8) +/- √((-8)^2 - 4*1*41) )/(2*1)`

Simplifying the above, we get

x =
`(8 +/- √(64 - 164) )/(2)`

x =
`(8 +/- √(-100) )/(2)`

[√-100 = √-1 *√100 = i*10 = 10i] because the value of √-1 = i]

x = (8 ± 10i )/2

Now dividing by 2, we get

x = 4 ± 5i

The answer is d) 4 ± 5i

Hope you will understand the concept.

Thank you.