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3 years ago

Without solving the equation, determine the nature of the roots of x^2 - 2x - 8 = 0.

Mathematics

1 answer:

noname [10]3 years ago

3 0

Answer:

two real, unequal roots

Step-by-step explanation:

This is a quadratic equation. The quadratic formula can be used to determine how many and what kind of roots may exist:

Find the discriminant, which is defined as b^2 - 4ac, if ax^2 + bx + c = 0. In this case, a = 1, b = -2 and c = -8, so that the discriminant value is

(-2)^2 - 4(1)(-8), or 4 + 32 = 36.

Because the discriminant is real and positive, we know for certain that we have two real, unequal roots

You might be interested in

Write the equation of a line in slope-intercept form that goes through the points (-4, 3) and (-5, 1). Show your work.

Neporo4naja [7]

M=1-3/-5-4
M=-2/-9
M=2/9

y=2/9x+c
let y=3 and x=-4
3=2/9<span>(-4)+c
3=-8/9+c
3+8/9=c
C=35/9

y=2/9x+35/9
</span>

7 0

3 years ago

In the figure below, O is between M and P, and N is the midpoint of MO. If =MP16 and =NO4, find OP.

Crazy boy [7]

Answer:

O is in between m and p so it is 6

Step-by-step explanation:

In the figure below, O is between M and P, and N is the midpoint of MO. If =MP16 and =NO4, find OP.

6 0

2 years ago

1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a

Sunny_sXe [5.5K]

Answer:

The equation $x=4$ represents in R^2 c) a line

The equation $x=4$ represents in R^3 a) a plane

The equation $y+3x=2$ represents in R^3 a) a plane

The equation $z-4y=8$ represents d) a plane

The pair of equations $y=2,z=8$ represents a) a line

Step-by-step explanation:

Let's start by studying each question :

In R^2 , $x=a$ with $a$ ∈ IR is the equation of all vertical lines

In this case, the only free variable is the variable ''y''

R^2 has two dimensions (x and y) so if we set $x=4$ we will have only one free variable in R^2 (which is a line in R^2). Therefore, $x=4$ represents a line in R^2

Now, in R^3 we have three dimensions (x, y and z) so if we set $x=4$ we will have only two free variables (y and z) and $x=4$ will represent a plane (which have two dimensions) in R^3.

2) The equation $y+3x=2$ in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.

The equation $y+3x=2$ in R^3 (given that we have two free variables) represents a plane.

Using the same reasoning, the equation $z-4y=8$ represents a plane (given that it has two free variables : ''y'' and ''x'')

Finally, the pair of equations $y=2,z=8$ set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.

The final answer is a) a line.

5 0

3 years ago

a group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the s

Liula [17]

Answer:

2/5 or 0.4

Step-by-step explanation:

10 students like building snowmen but do not like skiing

so students who like both building snowman and skiing = 60 - 10 = 50

Total number of students who does not like building snowman and also does not like skiing = 80 - 60 = 20

Therefore, the probability that a student who does not like building snowmen also does not like skiing = 20/50 = 0.4

6 0

3 years ago

Bus one had half of the grade eight students and 6 grade, seven students, bus two had 15 grade seven students and one-third of g

Rzqust [24]

I'm not sure about that one

7 0

3 years ago