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Nookie1986 [14]
3 years ago
8

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

Mathematics
2 answers:
Alinara [238K]3 years ago
3 0

Answer:

d) 4 ± 5i

Step-by-step explanation:

Here we have to use the quadratic formula.

x = \frac{-b +/- \sqrt{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 = \frac{-(-8) +/- \sqrt{(-8)^2 - 4*1*41} }{2*1}

Simplifying the above, we get

x = \frac{8 +/- \sqrt{64 - 164} }{2}

x = \frac{8 +/- \sqrt{-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.

ivolga24 [154]3 years ago
3 0

Answer:

Choice d is correct answer.

Step-by-step 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.

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\text{Distance traveled by steamboat}=20\text{ knots}\\\text{Distance traveled by yacht }=20+20=40\text{ knots}

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In Scientific notation, it would be: 5.8 × 10⁷ Km

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