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Andreyy89
2 years ago
15

Write the expression that appears under the radical symbol in the quadratic formula. what is the quality called? what can it be

used to determine?
Mathematics
1 answer:
ira [324]2 years ago
8 0
This expression is called the Discriminant, also shown as Δ.
It is equal to b² - 4ac. This is a very important part of the quadratic formula as it determines whether x will have two values, one repeated value or no real values. Here are a few examples.

a) x² - 2x - 1. a is equal to 1 since 1x² = x². b = -2, c = -1
The discriminant will be (-2)² - 4×1×-1 = 4 + 4 = 8.
Since Δ > 0, there are two x values. Graphed, the parabola sinks below the x axis.

b) x². a = 1, b = 0 (0x = 0), c = 0
The discriminant will be 0² - 4×1×0 = 0 - 0 = 0.
Since Δ = 0, there is only one x value. Graphed, the parabola touches the x axis at only one point.

c) x² + 1. a = 1, c = 1.
The discriminant will be 0² - 4×1×1 = 0 - 4 = -4
Since Δ < 0, there are no real x values. Graphed, the parabola floats above the x axis.

Hope this helps!
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How do I determine the intercepts of the line
patriot [66]

If my explanation doesn't make sense, there are some pretty good utube videos about it.

Here is our equation: 3x + 2y = 5

At the y-intercept (the point where the line meets y on a graph), x=0. The same can be applied to the x-intercept, as y=0. So, to find each intercept, we can treat 3x + 2y = 5, as we would with any other equation.

First, we will find the y-intercept. We know x=0, so that can be plugged in: 3(0) + 2y = 5

Anything times 0 is 0.

2y = 5

Divide both sides by 2 to isolate y:

y = 5/2 (or 2.5)

The y intercept is 5/2 (or 2.5).

Now, do the same for x, given that y=0: 3x + 2(0) = 5

Anything times 0 is 0.

3x = 5

Divide both sides by 3 to isolate x:

x = 5/3 (or 1.7

The x intercepts is 5/3 (or 1.7)

(You should probably use the fractional versions of the answers, but it depends on your teacher, I suppose)

Let me know if you have any questions about this! :)

8 0
2 years ago
Make q the subject of the formula 2(q+p) = 1+5q. Give your answer in the form ap-b/c where a,b and c are all positive integers
musickatia [10]

Answer:

\frac{2p-1}{3}

Step-by-step explanation:

Since you want to get q only and q appears in both side of the equation. Try to isolate q to one side.

1) Expand 2(q+p)

2q + 2p = 1 + 5q

2) Move all q terms to one side

5q - 2q = 2p - 1

3q = 2p - 1

3) Divide 3 on both side (to isolate q)

q = \frac{2p-1}{3}

8 0
3 years ago
The measure of angle S is ___ degrees. Round the number to the nearest degree.
Alex787 [66]
30 degrees because it's a 30-60-90
3 0
3 years ago
The bird house in your friend's yard casts a shadow that is 14 feet long. Your friend is 5 feet tall and casts a shadow that is
Kazeer [188]

Answer:

20 feet high

Step-by-step explanation:

Do the work

4 0
3 years ago
Read 2 more answers
The lenght of a rectangle is 4 cm less than three times the width. the perimeter is 64 cm
dybincka [34]
Let the width be x cm.
Then length=3x-4 cm.
Its perimeter is 64 cm.
We know that perimeter of a rectangle= 2(length+width)
So,
2(3x-4+x)=64
6x-8+2x=64
6x+2x=64+8
8x=72
x=9
Therefore,
length=(3×9-4)cm=(27-4)cm=23 cm.
Width=9 cm.
5 0
2 years ago
Read 2 more answers
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