Question

Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).

Answer 1

Real roots: -4, 1

Complex roots: 2-5i, 2+5i

Explanation:

(x²+3x-4)(x²-4x+29)

x²+3x-4=x²+4x-x-4=x(x+4)-(x+4)=(x-1)(x+4)

x²-4x+29 does not have real roots, since delta=16-4×29=-100<0.

However it has complex roots:

(4+/-10i)/2=2+/-5i

So the real roots are: -4 and 1

Complex roots: 2-5i, 2+5i

Answer 2

1

-4

2 + 5i

2 - 5i