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chubhunter [2.5K]
2 years ago
12

Consider the quadratic equation 2x² + 72 + k = 0. Which value of k results in the equation having complex solutions?​

Mathematics
1 answer:
postnew [5]2 years ago
5 0

Hi there!

\large\boxed{k> 6.125}

We can use discriminants to determine the value of k for which the equation would have complex solutions. (Those involving i)

If b² - 4ac < 0, then the equation will have complex solutions. Therefore:

Plug in the given values of b and a to solve:

7² - 4(2)(k) < 0

Simplify:

49 - 8k < 0

Solve the inequality:

49 < 8k

6.125 < k

k > 6.125. Anything greater than 6.125 would result in complex solutions.

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Given the points (5, 2) and (7, 10) find the slope of the line going through the two points . Now write the point-slope form of
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Step-by-step explanation:

the slope of a line is specified as the ratio y/x. that indicates how many units y changes, when x changes a certain amount of units.

so, going e.g. from (5, 2) to (7, 10), x changes from 5 to 7 = +2 units. and y changes from 2 to 10 = +8 units.

so, the slope y/x = m = 8/2 = 4

the point-slope form is

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(x1, y1) = coordinates of one point on the line. let's pick the first point (5, 2).

y - 2 = 4(x - 5)

or then fully simplified (leading to the slope- intercept form) :

y - 2 = 4x - 20

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for question 2 we do the same thing for (4, -2) and (0, -5).

x changes from 4 to 0, so, -4 units.

y changes from -2 to -5, so, -3 units.

slope = y/x = m = -3/-4 = 3/4

since there is a 0 included, let's use (0, -5) as point for the point-slope form

y - -5 = 3/4(x - 0)

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y + 5 = 3/4 x

so, the last option is correct.

3 0
2 years ago
SO basically uhh I suck at math
postnew [5]
Ok so you plug them in. -5 squared is 25 minus 27
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3 years ago
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