Question

2x^3-7x^2+x+6 one of the root is x=3 find the remaining roots. i got to this step 2x^2-x-2=0 i cant factor it so what do i do?

Answer 1

if you know a root is 3 syndivide it

3 | 2 -7 1 6
0 6 -3 -6
-----------
2 -1 -2 0

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

2*2 = 4

1,4; 2,2 neither subtract to -1 so complete the square/ quad formula it

Answer 2

-mid# sqrt(mid#^2 - 4(first)(last))
------ +- -----------------------
2(first#) 2(first#)

Answer 3

1/4
+- sqrt(1+16)/4

1/4 +- sqrt(17)/4

Answer 4

2x^2 -x -2 = 0
-------------
2

x^2 -(1/2)x -1 = 0

x^2 -(1/2)x + ___ = 1 + ___

x^2 -1/2x + 1/16 = 1 + 1/16

(x-1/4)^2 = 17/16

x- 1/4 = +- sqrt(17/16) = +-sqrt(17)/4

x = 1/4 +- sqrt(17)/4

Answer 5

i mean what happen to -1 and how is 1/16 come from

Answer 6

a complete square can change back and forth like this:

(x+2)^2 <--> (x^2 +4x +4)

right?

Answer 7

an incomplete square is stuck...

(x^2 +4x + ___ ) is stuck and cant change without first 'completing the square' right?

Answer 8

what we need are 2 numbers that add to 4 and multiply them together to get the missing term; but those 2 numbers have to be the SAME number.

3+1 cant work to complete the square
5-1 cant work to complete the square

we need to identical numbers in order to complete the square...

n+n = 4

2n = 4

n = 4/2 = 2

2+2 = 4; the missing term is the 2*2; which equals 4 right?

Answer 9

x^2 - 6x + ___ ??? we need to complete this square

n+n = -6

2n = -6

n = -6/2 = -3

since -3+-3 =-6; the missing term is -3.-3 = 9

x^2 -6x +9 is a complete square right?

Answer 10

yup! fantastic thank you very much!!