+0

0
300
3
+240

1. (a)  Use the fundamental theorem of algebra to determine the number of roots for  2x^2+4x+7.

(b)  What are the roots of 2x^2+4x+7? Show your work.

2. Consider the function f=(x)=x^3+2x^2-3 .

Graph the function.

What are the x- and y-intercepts of the graph?

3. Simplify the expression (x^3-5x^2+7x-12)÷(x-4) using long division. Show your work.

Nov 1, 2018

#1
+100458
+2

1)  (a)  There will be as many roots of a polynomial as its degree  [  some may be repeated roots ]

So....the number of roots here    = 2    since this is a second degree polynomial

(b)   2x^2 + 4x + 7  = 0     subtract 7 from both sides

2x^2 + 4x  =  - 7      factor out the 2 on the left

2 ( x^2 + 2x )   =  - 7    divide both sides by 2

x^2 + 2x  =  -7/2

Take 1/2 of 2  = 1...square it = 1....add it to both sides

x^2 + 2x + 1   =  -7/2 + 1      factor the left side, simplify the right

(x + 1)^2  = -5/2     take both roots

x + 1  =  ±√ [ - 5/2]  =  ±i √ 5 / √2  =   ±i √10 /2

x + 1  = ±i√10 / 2    subtract 1 from both sides

x =  -1 ±i√10 / 2

x =  [  -2  ± i √10 ]  / 2

Nov 1, 2018
edited by CPhill  Nov 1, 2018
#2
+100458
+2

2)  Here's the graph : https://www.desmos.com/calculator/hz0nsgeb2n

The x intercept   is  (1, 0)

The y intercept is (0, - 3)

Nov 1, 2018
#3
+100458
+2

(x^3-5x^2+7x-12)÷(x-4)

x^2   -  x    +  3

x - 4  [  x^3  -5x^2  + 7x  -  12  ]

x^3 - 4x^2

______________________

- x^2  +  7x

- x^2  + 4x

__________________

3x   -   12

3x   -   12

__________

The result is in red

Nov 1, 2018