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Cerrena [4.2K]
3 years ago
13

3x^2+kx=-3 What is the value of K will result in exactly one solution to the equation?

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0

Answer:

For k = 6 or k = -6, the equation will have exactly one solution.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = (x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

If \bigtriangleup = 0, the equation has only one solution.

In this problem, we have that:

3x^{2} + kx + 3 = 0

So

a = 3, b = k, c = 3

\bigtriangleup = b^{2} - 4ac

\bigtriangleup = k^{2} - 4*3*3

\bigtriangleup = k^{2} - 36

We will only have one solution if \bigtriangleup = 0. So

\bigtriangleup = 0

k^{2} - 36 = 0

k^{2} = 36

k = \pm \sqrt{36}

k = \pm 6

For k = 6 or k = -6, the equation will have exactly one solution.

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3 years ago
Mia is helping her glee club raise money to fund a field trip. The glee club secided to sell pencils, which come in boxes of 100
Nitella [24]

Answer:

m = 2500b

Step-by-step explanation:

As instructed,

let b = number of boxes sold

let m = total money made.

The total money made, is a function of the number of boxes sold.

Let me break this down:

There are 100 pencils in a box;

if they sold only one box, they will get 100 X $25 = $2500;

if they sold two boxes, they will get 200 X $25 = $5000;

if they sold three boxes, they will get 300 X $25 = $7500;

Following the trend, we can deduce that money made, m = (number of boxes sold X 100 ) X $25

representing this using the variables we were given, we have

m = 100b X 25

hence

m = 2500b

7 0
2 years ago
Pls Helpp!!! "Nancy currently has $50.75 in her bank account and plans on depositing $11.25 into the account each week. She plan
Savatey [412]

Answer:

Step-by-step explanation:

w = (197-50.75)/11.25 = 13

3 0
3 years ago
Suppose a triangle has two sides of length 33 and 37 and that the angle between these two sides is 120 what is the length of the
Nutka1998 [239]

Answer:

  60.65

Step-by-step explanation:

The Law of Cosines can help you figure this out. Call the given sides "a" and "b" and the given angle "C". Then the third side, "c" will satisfy the relation ...

  c² = a² + b² -2ab·cos(C)

  = 33² +37² -2·33·37·cos(120°) = 3679

  c = √3679 ≈ 60.65476 ≈ 60.65

The length of the third side is about 60.65 units.

5 0
3 years ago
Simplify 3 over 2 x 3 over 2 exact answer
nikitadnepr [17]

ANSWER : 9 over 4

or 2 and 1/4

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

*3 over 2 x 3 over 2 is 3/2 x 3/2* << this is for me to remember

Okay so multiplying fractions means for us to multiply across. That means if we line the fractions, we multiply. Like this

 3     x     3

-----         -----                3 times 3 is = 9

 2     x     2                  2 times 2 is = 4

9 over 4 is the same thing as 2 and 1/4  << FRACTION    

                                                ^^      

                                           WHOLE

Hope I helped (:

8 0
3 years ago
Read 2 more answers
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