Write a quadratic equation, in standard form, that has roots 8 and 11.

x² - 19 x + 88

Step-by-step explanation:

Standard form of quadratic equation is

a x² + b x + c = 0  

We can factorize this equation

a x² + b x + c = a (x - x₁) · (x - x₂)

where x₁ and x₂ are the roots of the equation

In this case we have roots x₁ = 8 and x₂ = 11

(x - 8) (x - 11) = x² - 11 x - 8 x + (-8) · (-11) = x² - 19 x + 88 = x² - 19 x + 88

x² - 19 x + 88

God with you!!!

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}