Ask question

Ask question

All categories

3 years ago

12

The quadratic equation 2x^2 + bx + 18 = 0 has a double root. Find all possible values of b.

1 answer:

Doss [256]3 years ago

4 0

When a quadratic equation ax^2+bx+c has a double root, the discriminant,
D=b^2-4ac=0
Here
a=2,
b=b,
c=18
and
D=b^2-4ac=b^2-4*2*18=0
solve for b
b^2-144=0
=> b= &pm; sqrt(144)= &pm; 12

So in order that the given equation has double roots, the possible values of b are &pm; 12.

You might be interested in

Anna starts a fixed deposit with $178000, the bank offers 9.5% per year simple interest for 8 months. she has the option of rest

soldier1979 [14.2K]

Using simple interest, we have that:

A) The interest due after 8 months is $11,272.33.

B) The total value of the investment will be of $189,986.24.

The amount of interest earning using <em>simple interest</em>, after <u>t years</u>, with an <u>yearly interest rate of i</u> and an <u>initial investment of P</u> is given by:

$E = Pit$

In this problem:

Deposit of $178,000, hence $P = 178000$ .
Interest rate of 9.5% per year, hence $i = 0.095$ .
8 months, the time is in years, hence $t = \frac{8}{12} = \frac{2}{3}$

Item a:

$E = Pit$

$E = 178000(0.095)\frac{2}{3} = 11272.33$

The interest due after 8 months is $11,272.33.

Item b:

For the second interest, we consider $P = 11272.33$ , hence:

$E_2 = Pit$

$E_2 = 11272.33(0.095)\frac{2}{3} = 713.91$

The total value will be composed by:

The initial deposit of $178,000.
The first interest of $11,272.33.
The second interest of $713,91.

Hence, it will be:

$T = 178000 + 11272.33 + 713.91 = 189986.24$

The total value of the investment will be of $189,986.24.

A similar problem is given at brainly.com/question/13176347

3 0

3 years ago

Which expression represents -8x2 + 54x + 140 in factored form?

ra1l [238]

Answer:

-2(x+2)(4x-35)

Step-by-step explanation:

Factor out the 2 and by grouping.

3 0

3 years ago

if a population doubles every 5 years how many years would it take for the population to increase by 10 times original amount?

Alecsey [184]

25 years is the answer

7 0

3 years ago

A boat traveled 37 miles in 2 hours. At this<br> rate, how many miles will the boat travel in

Inessa [10]

<u><em>Answer:</em></u>

i. The boat will travel 18.5 miles in one hour

ii. The boat will travel 9.25 miles in half an hour

iii. The boat will travel 27.75 miles in one and a half hours

<u><em>Explanation:</em></u>

We are given that the boat travel 37 miles in 2 hours

To get the miles traveled, we can simply use cross multiplication

<u>i. Miles traveled by the boat in one hour:</u>

37 miles .....................> 2 hours

x miles ........................> 1 hour

$x = \frac{37*1}{2}=18.5$ miles

<u>ii. Miles traveled in half an hour:</u>

37 miles .....................> 2 hours

x miles ........................> 0.5 hour

$x = \frac{37*0.5}{2}=9.25$ miles

<u>iii. Miles traveled in an hour and a half:</u>

37 miles .....................> 2 hours

x miles ........................> 1.5 hour

$x = \frac{37*1.5}{2}=27.75$ miles

Hope this helps :)

8 0

4 years ago

The graph of a system of equations is shown below.which ordered pair is the best estimate for the solution to the system of equa

ivanzaharov [21]

Answer:

B. (-3, 2)

Step-by-step explanation:

The solution is given by the coordinates of the point where the lines intersect.

From the graph we see that it is the point where x = -3 and y = 2.

5 0

4 years ago

Read 2 more answers