All categories

3 years ago

How many solutions does this equation have x^4 - 6x^2 -7 = 0

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

5 0

Answer:

2 solutions

Step-by-step explanation:

x^4-6x^2-7=0

Replace x^2 by y

(x^2)^2-6x^2-7=0

y^2-6y-7=0

D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64

sqrtD=8

y1=(-b-sqrtD)/2a=-2/2=-1

y2= (-b+sqrtD)/2a=14/2=7

x^2=-1(n0 roots) x^2=7 x=sqrt7 or x=-sqrt7

2 roots

You might be interested in

Simplify this equation Thanks a lot!!!

den301095 [7]

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

$\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}$

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

$\bf\implies a^m \times b^m = (ab)^m$

Using this property , we have ,

$\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}$

This can be written as ,

$\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}$

Simplifying using ( a+b)(a-b) = a² - b² ,

$\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}$

Subtracting the numbers inside the brackets ,

$\rm\implies (-1)^{2n - 1 }$

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the power is odd .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

$\rm\implies\boxed{\quad \red{ -1 }\quad }$

Hence the required answer is (-1) .

4 0

3 years ago

kell works at an after-school program at an elementray school. on monday he work for 1.5 hours and recived 12.6 dollars, on tues

Rina8888 [55]

Answer:

Kell would make more money working 10 hours than Markio.

Step-by-step explanation:

To find how much Kell makes per hour, you have to divide how much he worked by how much he earned. So on Monday, Kell worked 1.5 hours and received 12.6 dollars. Divide 12.6/1.5 and you'll find you're answer.

Monday: 12.6/1.5=8.4

On Tuesday, the problem states that he worked 2.5 hours and received 21 dollars. Divide 21/2.5 and you'll find the answer.

Tuesday: 21/2.5= 8.4

On Wednesday, the problem states that he worked 4 hours and received 33.60. Divide 33.60/4 and you'll get you're answer.

Wednesday: 33.60/4= 8.4

So we can conclude that Kell makes $8.40 per hour.

Now the problem states, Markio gets paid 7 dollars per hour. To find the answer to the question, you have to multiply how much they make per hour times 10 hours.

Markio: 7x10=70

Kell: 8.4x10=84

So to answer the question, Kell would make more money working 10 hours.

Hope it helps!

3 0

3 years ago

Jack can read 45 pages of his book in one and half hours. At the rateb, how long will it take jack to read the entier 300 page b

Brrunno [24]

Answer:

10 hours

Step-by-step explanation:

45 pages=1.5 hours

300=x

x=300*1.5/45

x=10

5 0

3 years ago

A cylinder has a base area of 100cm and volume of 1500 cm what’s the height

e-lub [12.9K]

Answer:

we know,

Volume of cylinder = Base area × height

1500= 100×h

so, Height h = 15 cm

6 0

2 years ago

What are the solutions to the equation x2 +3x-4=0

Serhud [2]

$x^{2} +3x-4=0$

You wan't to get it into a format of (x+a)(x+b)=0
where a+b = 3 (the one from the 3x)
and where a*b= -4 (from the last -4)

(x+4)(x-1)=0
See how 4+(-1) = 3 and (4)(-1) = -4

now find what values of x would make the equation equal 0
x=-4
(-4+4)(-4-1) = (0)(-5) = 0

x=1
(1+4)(1-1) = (5)(0) = 0

4 0

3 years ago

Read 2 more answers