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bearhunter [10]
3 years ago
11

What are the key features of a graph of a quadratic equation with only complex solutions

Mathematics
1 answer:
dybincka [34]3 years ago
4 0

Answer:

If  D< 0, the roots of the quadratic equation will b complex.

Step-by-step explanation:

Let ax^{2}  + bx + c =0 is the given quadratic equation.

So, if the Discriminant (D) = b^{2}  - 4ac  < 0, the the equation will have only complex solutions.

Complex roots are represented in the form of (x \pm iy)

1.  <u> x represents the X axis (real) co ordinate,</u>

    <u>y represents the Y axis (imaginary) coordinate</u>

<u />

<u />

2. Also, the graph of the with equation  D < 0  NEVER CROSSES the X - axis, as there are no real roots of the equation, only complex roots.

3. Here. roots are always identical but are opposite in signs. Such pair or roots with opposite sign are called CONJUGATE PAIRS.

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1. Hannah gives clues about her 6 digit secret number:
Ulleksa [173]
1.  This is a rule which helps a person identify if a number is divisible by nine.
There is no specific answer to why this is observed but I believe that is just how multiples of nine and three behave!

It is the same with the multiples of three as well!

By the way the 6 digit number could be 513315
thanks, hope that helps!!
8 0
3 years ago
2. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm
4vir4ik [10]

Answer:

It's required 7.48\ m^2 of sheet for the tank

Step-by-step explanation:

<u>Surface Area of a Cylinder</u>

Given a right cylinder of base radius r and height h, the surface area is calculated as follows:

S=2\pi r^2+2\pi r h

The cylindrical tank has a height of h=1 m and a base diameter of 140 cm. The radius is half the diameter, thus r=140/2 = 70 cm = 0.7 m. Substituting:

S=2\pi 0.7^2+2\pi (0.7)(1)

S=2\pi 0.49+1.4\pi

S=2.38\pi

\boxed{S=7.48\ m^2}

It's required 7.48\ m^2 of sheet for the tank

7 0
3 years ago
A concrete stepping stone measures 20 square inches. What is the area of 30 such stones
Natalka [10]
The answer is 600. 30•20
7 0
3 years ago
Find the function of which is the solution of 36y"-48y'-48y=0 with initial conditions y1(0)=1. y1'(0)=0
lilavasa [31]

Answer:

y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }

Step-by-step explanation:

Let,  D=\frac{d}{dx}

Now, us simplify the given differential equation and write it in terms of D,

36y''-48y'-48y=0

or, 3y''-4y'-4y=0

or, (3D^2-4D-4)y=0

We have our auxiliary equation:

3D^2-4D-4=0

or, (3D+2)(D-2)=0

or, D=2, - \frac{2}{3}

Therefore our solution is,

y=Ae^{2x}+Be^{- \frac{2}{3}x}

and, y'=2Ae^{2x}-\frac{2}{3}Be^{\frac{2}{3}x }

Applying the boundary conditions, we get,

A+B=1

2A-\frac{2}{3}B=0

Solving them gives us,

A=\frac{1}{4} ,B=\frac{3}{4}

Hence,

y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }

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3 years ago
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