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

we have

To find the roots of g(x)

Find the roots of the first term and then find the roots of the second term

Step 1

Find the roots of the first term

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

Square root both sides

so the factored form of the first term is

Step 2

Find the roots of the second term

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

Remember that

Square root both sides

so the factored form of the second term is

Step 3

Substitute the factored form of the first and second term in g(x)

therefore

the answer is

the roots are

the correct answer is the second option

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step-by-step explanation: