Answer:
x1=1
x2= -4
x3= (2 + 5i)
x4= (2 - 5i)
Explanation:
STEP 1-
Find the roots of the first term.
(x^2 + 3x -4)=0
Then group the terms that contain the same variable, and move the constant to the opposite side of the equation.
(x^2 + 3x)=4
Complete the square. Remember to balance the equation by adding the same constants to each side.
(x^2 + 3x + 1.5^2)=4 + 1.5^2
(x^2 + 3x + 1.5^2)=6.25
Rewrite as perfect squares
(x + 1.5)^2=6.25
Square root both sides.
(x + 1.5) = (+/-)2.5
x= -1.5(+/-)2.5
x= -1.5 + 2.5 = 1
x= -1.5 + 2.5= -4
so the factored form of the first term.
(x^2 + 3x + 4) = (x - 1) (x + 4)
STEP 2-
Find the roots of the second term
(x^2 - 4x + 29)= 0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x^2 - 4x)= -29
Complete the square. Remember to balance the equation by adding the same constants to each side
(x^2 - 4x + 4) = - 29 + 4
(x^2 -4x + 4) = -25
Rewrite as perfect squares
(x - 2)^2 = -25
Remember that
i = square root of -1
Square root both sides
(x - 2) = (+/-)5i
x= 2 (+/-)5i
x= 2 + 5i
x= 2 - 5i
so the factored form of the second term is
(x^2 - 4x + 29) = (x - (2 + 5i))(x - (2 - 5i))
STEP 3-
Substitute the factored form of the first and second term in g(x)
g(x) = (x-1)(x + 4)(x- (2+ 5i))(x- ( 2-5i)
there for you have your answers