Final answer:
To solve the quadratic equation 2r² - 3r - 5 = 0 using the quadratic formula, substitute the values of a, b, and c into the formula and simplify.
Step-by-step explanation:
To solve the quadratic equation 2r² - 3r - 5 = 0 using the quadratic formula, we need to first identify the values of a, b, and c in the equation ax² + bx + c = 0.
In this case, a = 2, b = -3, and c = -5.
Substituting these values into the quadratic formula, we have:
r = (-b ± √(b² - 4ac))/(2a)
Plugging in the values, we get:
r = (-(-3) ± √((-3)² - 4(2)(-5)))/(2(2))
Simplifying further, we get:
r = (3 ± √(9 + 40))/4
r = (3 ± √49)/4
r = (3 ± 7)/4
So, the solutions are:
r = (3 + 7)/4 = 10/4 = 2.5
r = (3 - 7)/4 = -4/4 = -1