Final answer:
The quadratic equation v²+5v+6=0 is solved using the quadratic formula, yielding two solutions: v = -2 and v = -3.
Step-by-step explanation:
To solve the quadratic equation v²+5v+6=0, we can use the quadratic formula, which is applicable to any equation of the form ax²+bx+c = 0. The solution or roots for a quadratic equation are given by the formula:
x = ∛(-b ± √(b²-4ac))/(2a)
For our equation, a=1, b=5, and c=6. Plugging these values into the quadratic formula yields:
x = ∛(-5 ± √((5)²-4(1)(6)))/(2(1))
This simplifies to:
x = ∛(-5 ± √(25-24)) / 2
x = ∛(-5 ± 1) / 2
So the two solutions are:
x = (-5 + 1) / 2 = -2
and
x = (-5 - 1) / 2 = -3
Thus, the quadratic equation v²+5v+6=0 has two solutions: v = -2 and v = -3.