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3 years ago

If a quadratic equation has a real root, what do you know about the other roots of the equation? Explain.

Mathematics

1 answer:

notsponge [240]3 years ago

7 0

Answer:

A Quadratic Equation can have upto 2 roots maximum. So,if one of the roots is a Real number, there are following two possibilities:

1) The other root is also a real number, but a different number

2) Its a repeated root, so the other root is the same number.

The other root cannot be a complex number as its not possible for one root to be real and other to be complex. Either no root will be complex or both will be complex roots.

Following are 3 possibilities for the roots of a quadratic equation:

2 Real and Distinct roots
2 Real and Equal roots
2 Complex roots

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Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 969696

Scilla [17]

Answer:

See explanation.

Step-by-step explanation:

Hi, you provided a very limited information to enable us answer your question.

From the given information, this is what we can help you with.

The total annual cost is

$y = 3x + 96$

because there is a fixed cost of $96 and there is an additional charge of $3 per books borrowed.

If Aaden borrow x books, the total cost will be

$y = 3x + 96$

8 0

3 years ago

Read 2 more answers

A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section)

dolphi86 [110]

Answer:

radius r = 47/π in

length l = 23.5 in

Step-by-step explanation:

Let us recall that:

Volume of a cylinder = $\pi r^2 h$ --- (1)

The girth g = $2 \pi r + h$ ----- (2)

Given that:

height (h) + girth (g) = 141

Then g = 141 - h ----- (3)

Equating equation (2) and (3), we have:

141 - h = 2πr + h

2h = 141 - 2πr

h = 70.5 - πr ------ (4)

From, here now, we can now replace the value of h into equation (1)

i.e.

V = πr²(70.5 - πr)

V = 70.5πr² - π²r³

Taking the differential of the above equation with respect to r, we have:

$\dfrac{dv}{dr} = 141 \pi r- 3\pi ^2 r^2$

By further differentiation:

$\dfrac{d^2v}{dr^2} = 141 \pi - 6\pi ^2 r$

Let set $\dfrac{dv}{dr}= 0$ , Then:

141πr - 3π²r² = 0

141πr = 3π²r²

Divide both sides by πr

141 = 3πr

r = 141/3π

r = 47/π in

Replacing the value of r = 47/π into equation (4), we have:

h = 70.5 - πr

h = 70.5 - π(47/π)

h = 70.5 - 47

h = 23.5 in

From equation (3);

h + g = 141

23.5 + g = 141

g = 141 - 23.5

g = 117.5 in

Volume = πr²h

V = π × (47/π )² × 23.5

V = 16523.94 in³

4 0

3 years ago

F=1.8c+32 the high temperature in a mountain city was 15c what is the high temperature in degrees Fahrenheit

ololo11 [35]

F = (1.8 x 15) +32
F = (27) + 32
F = 59

5 0

3 years ago

What is the number if 6/7 of 28 is equal to 30% of that number.

makkiz [27]

Answer:

80 is the actual number

Step-by-step explanation:

(28/7)(6)=24

24 x 100=2400

2400/30=80

80 x .3 = 24

5 0

3 years ago

According to industry sources, online banking is expected to take off in the near future. The projected number of households (in

Airida [17]

Answer:

(a) The least-square regression line is: $y=4.662+2.709x$ .

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

$y=\alpha +\beta x$

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

(a)

The formula to compute intercept and slope is:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}$

The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.

Compute the value of intercept and slope as follows:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}$

The least-square regression line is:

$y=4.662+2.709x$

(b)

For the year 2007 the value of x is 10.

Compute the value of y for x = 10 as follows:

$y=4.662+2.709x$

$=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8$

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

5 0

3 years ago