Question

Quadratic Equation [S^2 +7/4}S =1/2

a) S = 1/2, -3/2
b) S =1/2, 3/2
c) S = 1}/4, -3/4
d) S =1/4, 3/4

Answer 1

To solve the quadratic equation, use the quadratic formula S = (-b ± √(b² - 4ac)) / 2a. Substitute the values a = 1, b = 7/4, and c = 1/2 into the formula and simplify to find the solutions.

Step-by-step explanation:

In order to solve the quadratic equation, we need to use the quadratic formula: S = (-b ± √(b² - 4ac)) / 2a. For the given equation, we have a = 1, b = 7/4, and c = 1/2. Substituting these values into the quadratic formula, we get:

S = (-7/4 ± √((7/4)² - 4(1)(1/2))) / (2(1))

Simplifying the equation further, we have:

S = (-7/4 ± √(49/16 - 4/2)) / 2

S = (-7/4 ± √(49/16 - 8/4)) / 2

S = (-7/4 ± √(41/16)) / 2

S = (-7/4 ± (1/4)√41) / 2

Therefore, the solutions to the quadratic equation are: S = (-7/4 + (1/4)√41) / 2 and S = (-7/4 - (1/4)√41) / 2