Question

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

Answer 1

(a)

the theorem states that for a polynomial of degree n there are n roots. However they may be complex.

2x² + 4x + 7 is a polynomial of degree 2 ( indicated by largest exponent of the polynomial )

Hence there are 2 roots

(b)

To solve use the quadratic formula

x = ( - b ±√(b² - 4ac) ) / 2a

with a = 2, b= 4 and c = 7

x = (- 4 ± √(16 - 56) ) / 4

  = (- 4 ± √(- 40 ) ) / 4

  = ( - 4 ± 2i√10) / 4

  = - 1 ± $\frac{1}{2}$ i√10