Solve the quadratic equation using factorisation method: 5c^2+5c+3=0

Answer 1

To solve the quadratic equation 5c^2 + 5c + 3 = 0 using factorization method:

Step 1: Multiply the coefficient of c^2 (5) by the constant term (3). In this case, 5 * 3 = 15.

Step 2: Find two numbers that multiply to give the result from step 1 (15) and add up to the coefficient of c (5). In this case, there are no two numbers with that property.

Since the quadratic equation cannot be easily factored, we can use the quadratic formula to find the solutions. The quadratic formula is given as c = (-b ± √(b^2 - 4ac)) / 2a.

For the equation 5c^2 + 5c + 3 = 0, the coefficients are a = 5, b = 5, and c = 3. Substituting these values into the quadratic formula, we get:

c = (-5 ± √(5^2 - 4 * 5 * 3)) / (2 * 5)

Simplifying further:

c = (-5 ± √(25 - 60)) / 10
c = (-5 ± √(-35)) / 10

The discriminant (√(25 - 60)) is negative, indicating that there are no real solutions. Therefore, the given quadratic equation 5c^2 + 5c + 3 = 0 has no real solutions.