Final answer:
The quadratic equation with roots √3 + 1/2 and √3 − 1/2 is x² - 2√3x + 11/4 = 0.
Step-by-step explanation:
The question is asking us to find the quadratic equation with the given roots √3 + 1/2 and √3 − 1/2. To find this quadratic equation, we can use the fact that if α and β are the roots of the quadratic equation ax2+bx+c=0, then the sum of the roots (α + β) is equal to -b/a and the product of the roots (αβ) is equal to c/a.
First, we find the sum of the roots: (√3 + 1/2) + (√3 − 1/2) = 2√3. Next, we find the product of the roots: (√3 + 1/2)(√3 − 1/2) = (√3)2 - (1/2)2 = 3 - 1/4 = 11/4.
Now, if the coefficient of x2 (a) is 1, we would have the equation x2 - (sum of roots)x + (product of roots) = 0. Thus, our quadratic equation is x² - 2√3x + 11/4 = 0.