Answer:
Given that one root is 1/2 + √5, we can assume the other root to be its conjugate, 1/2 - √5. Now, using the sum and product of roots, we can construct the quadratic equation. Therefore, the quadratic equation with rational coefficients whose one root is 1/2 + √5 is 4x² - 4x - 19 = 0.
Step-by-step explanation:
Given that one root is 1/2 + √5, we can assume the other root to be its conjugate, 1/2 - √5. Now, using the sum and product of roots, we can construct the quadratic equation. Therefore, the quadratic equation with rational coefficients whose one root is 1/2 + √5 is 4x² - 4x - 19 = 0.
