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3 years ago

How many solutions can a quadratic equation have and why does it vary? How would the corresponding graphs look like?

Mathematics

1 answer:

tino4ka555 [31]3 years ago

3 0

Hello from MrBillDoesMath!

Answer:

0, 1, or 2

Discussion:

Examples:

1) x^2 + 9 = 0 has 0 solutions over the real numbers

2) x^2 + 9 = 0 has 2 solutions over the complex number ( 3i, -3i)

3) the quadratic (x-3)^2 = 0 has a single solution, x = 3, of multiplicity two. (which some regard as two solutions).

The bottom line is the number of roots is given by the quadratic solution

( -b +\- sqrt( b^2 - 4ac) ) /2a

In particular if the discriminant (b^2 -4ac) = 0, the quadratic has one solution. If the discriminant is >0 there are two (real) solutions, and if the discriminant is <0 there are 2 imaginary (complex) solutions.

Thank you,

MrB

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Help please!!! Find the sum of the series show your work

AleksAgata [21]

Answer:

$\sum_{i=1}^{12}(3i-1) = 222$

Step-by-step explanation:

The given series is

$\sum_{i=1}^{12}(3i-1)$

The first term is

$f(1) = 3 \times 1 - 1 = 2$

The last term is

$f(12) = 3 \times 12 - 1 = 35$

To find the number of terms in the sequence, solve,

$3i - 1 = 35$

$3i = 36 \\ i = 12$

The sum of the first i-terms of an arithmetic sequence is:

$S_i = \frac{i}{2} (f(1) + f(2))$

We substitute the values to get;

$S_ {12}= \frac{12}{2} (2+ 35)$

$S_ {12}=6(37)$

$S_ {12}= 222$

6 0

4 years ago

Find the midpoint of AB. 1. (4.5, 4.5) 2. (1.5, 1.5) 3. (3, 3) 4. (2, 2)

eimsori [14]

Answer:

2. (1.5, 1.5)

Step-by-step explanation:

midpoint = (x1+x2)/2 , (y1+y2)/2

A = (-3,-3) and B = (6,6)

midpoint = (-3+6)/2, (-3+6)/2

= 3/2 , 3/2

5 0

3 years ago

Which equation has the components of 0 = x2 – 9x – 20 inserted into the quadratic formula correctly?

Aneli [31]

Answer:

The required equation is $x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-20)}}{2(1)}$ .

Step-by-step explanation:

If a quadratic equation is $ax^2+bx+c=0$ , then the quadratic formula is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given quadratic equation is

$x^2-9x-20=0$

Here, a=1, b=-9 and c=-20.

Substitute a=1, b=-9 and c=-20 in the above quadratic formula.

$x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-20)}}{2(1)}$

Therefore the required equation is $x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-20)}}{2(1)}$ .

6 0

3 years ago

Read 3 more answers

Can anyone help me, i will give brainiest.

laila [671]

Answer: ∠DOB: 48°

Step-by-step explanation:

1. we need an equation first. the sum of all angles (108°, n°, 2n°) is equal to 180°. we can depict this with the equation: 108°+2n°+n°=180°

2. now we can solve for the missing variable, n.

108°+3n°=180° → subtract both sides by → 3n°=72° → divide both sides by 3 → n=24°

3. now that we know that n=24°, we can solve the value of ∠DOB. we can see that ∠DOB is 2n° which we just plug the number we got for n into the equation. 2*24=48° meaning ∠DOB is 48°

hope this heped! ♡

7 0

2 years ago

Read 2 more answers

PLEASE HELP

MAXImum [283]

The nth term of any geometric sequence can be expressed as:

a(n)=ar^(n-1), a(n)=nth term, a=initial term, r=common ratio, n=term number...

We can easily see that the first term, a=-8

The common ratio is 4/-8=-2/4=1/-2=r=-1/2 so the rule is:

a(n)=-8(-1/2)^(n-1) so the tenth term is:

a(10)=-8(-1/2)^(10-1)

a(10)=-8(-1/2)^9

a(10)=1/64

5 0

3 years ago