Final answer:
To factorize the trinomial x² + 5x + 25/4, we can use the quadratic formula or completing the square method. However, after applying the formula, we find that the trinomial does not factorize into linear factors.
Step-by-step explanation:
To factorize the trinomial x² + 5x + 25/4, we can use the quadratic formula or completing the square method. Let's use the quadratic formula to find the roots of the trinomial. The quadratic formula is given by:
x = (-b ± √(b² - 4ac))/(2a)
For the given trinomial, a = 1, b = 5, and c = 25/4. Substituting these values into the quadratic formula:
x = (-5 ± √(5² - 4*1*(25/4)))/(2*1)
Simplifying the equation further, we get:
x = (-5 ± √(25 - 25))/(2)
x = (-5 ± √0)/(2)
x = (-5 ± 0)/(2)
Therefore, the trinomial x² + 5x + 25/4 does not factorize into linear factors.
Learn more about Factorizing Trinomials