Final answer:
To find the values of the given expressions using the roots of the equation, we first use the quadratic formula to find the roots a and b. Then, we substitute these roots into the expressions to calculate the values.
Step-by-step explanation:
To find the values of the given expressions using the roots of the equation, 4x²+x+3=0, we need to first find the values of a and b, which are the roots.
Using the quadratic formula, we can find the roots of the equation.
x = (-b ± √(b²-4ac))/(2a)
Plugging in the values a=4, b=1, and c=3 into the formula, we can solve for x to find the values of a and b.
Once we have the values of a and b, we can substitute them into the expressions given to calculate the values.
1) (a⁴b-ab⁴)² = ((a^4)(b)-(ab^4))^2
2) a²+b²÷ab = (a^2+b^2)/(ab)