Question

Find the solution(s) to 2x²−5x–3=0. Check all that apply.

a. x=2
b. x=−21​
c. x=21​
d. x=3
e. x=−3

Answer 1

To solve the quadratic equation 2x² - 5x - 3 = 0, we use the quadratic formula. The solutions are x = 3 and x = -3/2. Option d (x = 3) is a solution, but options a, b, c, and e are not solutions.

Step-by-step explanation:

To solve the quadratic equation 2x² - 5x - 3 = 0, we can use the quadratic formula. This formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the equation. In this case, a = 2, b = -5, and c = -3. Plugging these values into the formula, we get:

x = (-(-5) ± √((-5)² - 4(2)(-3))) / (2(2))

x = (5 ± √(25 + 24)) / 4

x = (5 ± √49) / 4

x = (5 ± 7) / 4

So the two solutions are x = (5 + 7) / 4 = 3 and x = (5 - 7) / 4 = -3/2.

Checking the given options, we find that option d (x = 3) is a solution to the equation, but options a (x = 2), b (x = -21), c (x = 21), and e (x = -3) are not solutions to the equation.