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luda_lava [24]
3 years ago
11

Explain the difference between quadratic equations with one solution, two solutions, and complex solutions

Mathematics
1 answer:
shusha [124]3 years ago
4 0
Recall that given the equation of the second degree (or quadratic)
 ax ^ 2 + bx + c
 Its solutions are:
 x = (- b +/- root (b ^ 2-4ac)) / 2a
 discriminating: 
 d = root (b ^ 2-4ac)
 If d> 0, then the two roots are real (the radicand of the formula is positive). 
 If d = 0, then the root of the formula is 0 and, therefore, there is only one solution that is real and of multiplicity 2 (it is a double root).
 If d <0, then the two roots are complex and, in addition, one is the conjugate of the other. That is, if one solution is x1 = a + bi, then the other solution is x2 = a-bi (we are assuming that a, b, c are real).
 One solution:
 A cut point with the x axis
 Two solutions:
 Two cutting points with the x axis.
 Complex solutions:
 Does not cut to the x axis
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3 years ago
Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.
Natali [406]
The answer to what the length of the leg would be is 15.

You would do this problem by first writing down your Pythagorean Theorem, which is a^2 + b^2 = c^2.

Since we have our hypotenuse which is c^2 in our equation, we would write or insert the number we have.

So our equation could be that a or b leg equals 20, it doesn’t matter which one.

So we could write, 20^2 + b^2 = 25^2. So we don’t know what b leg is.

First we should figure out what 20^2 is and what 25^2 is.

20^2 is 400 and 25^2 is 625.

Our equation now comes to 400 + b^2 = 625.

Now we take 400 and subtract it from
625 -> 400 + b^2 = 625
-400.

So 625 - 400 comes out to be 225.

Lastly instead of squaring or putting 225 to the second power, we do the opposite.

So instead of squaring 225 we must square root 225. √ 225 .

The square root of √ 225 comes out to be 15.

3 0
3 years ago
Assume that Brad makes an initial investment of $2,000. Use your formula to find the final balance of the savings account after
svetlana [45]

Answer:

The formula is 2000 x (1 + Rate/100)^15

5 0
3 years ago
In ∆GHI, the measure of I=90°, the measure of G=82°, and GH = 3.4 feet. Find the length of HI to the nearest tenth of a foot.​
natka813 [3]

Answer: 3.4

Step-by-step explanation:

i got this problem on delta math

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What are the important things an 8th grader needs to know about math?
gogolik [260]
Always foucus on the teacher ask help when needed
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