(a) Use the fundamental theorem of algebra to determine the number of roots for .

(b) What are the roots of ? Show your work.

SamJones
Feb 7, 2018

#1**+1 **

a. The fundamental theorem says that a polynomal of degree "n" will have "n" roots

Note that some may be repeated and/or some may be complex

So.....this a polynomial of degree 2....so...it will have two roots

b.

2x^2 + 4x + 7 = 0

Use the quadratic formula a = 2, b = 4, c = 7

So we have

x_{1,2} = [ - 4 ± √ [4^2 - 4(2)(7) ] ] / [ 2 * 2 ] =

[ -4 ± √ [ 16 - 56] ] / 4 =

[ -4 ± √ -40 ] / 4 =

[ - 4 ± 2i√ 10 ] / 4 =

[ -2 ± i√ 10 ] / 2

CPhill
Feb 7, 2018