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Ugo [173]
2 years ago
11

Solve 5x^2 − 3x + 17 = 9.

Mathematics
1 answer:
Vedmedyk [2.9K]2 years ago
7 0

Answer:

The roots of the equation are x = \frac{3+\sqrt{151}i}{10} and x = \frac{3-\sqrt{151}i}{10}

and there are no real roots of the equation given above

Step-by-step explanation:

To solve:

5x² − 3x + 17 = 9

or

⇒ 5x² − 3x + 17 - 9 = 0

or

⇒ 5x² − 3x + 8 = 0

Now,

the roots of the equation in the form ax² + bx + c = 0 is given as:

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

in the above given equation

a = 5

b = -3

c = 8

therefore,

x = \frac{-(-3)\pm\sqrt{(-3)^2-4\times5\times8}}{2\times5}

or

x = \frac{3\pm\sqrt{9-160}}{10}

or

x = \frac{3+\sqrt{-151}}{10} and x = \frac{3-\sqrt{-151}}{10}

or

x = \frac{3+\sqrt{151}i}{10} and x = \frac{3-\sqrt{151}i}{10}

here i = √(-1)

Hence,

The roots of the equation are x = \frac{3+\sqrt{151}i}{10} and x = \frac{3-\sqrt{151}i}{10}

and there are no real roots of the equation given above

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3 years ago
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Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2 3 of the way there.
DochEvi [55]

Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2/3 of the way there.   How many more hours  does Liza have to drive?

<em><u>Answer:</u></em>

Liza need to drive 2 more hours to reach her sister house

<em><u>Solution:</u></em>

Given that Liza is driving to her sister's house 360 miles away

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After 4 hours, Liza is 2/3 of the way there.

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So Liza has covered 240 miles in 4 hours

Let us find the speed

<em><u>The relation between distance and speed is given as:</u></em>

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Now distance = 120 miles and speed = 60 miles per hour

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Step-by-step explanation:

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