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

Answer 1

To solve the quadratic equation 2c^2 + 5c + 3 = 0 using the factorization method, we need to factorize the quadratic expression and set each factor equal to zero.

Given equation: 2c^2 + 5c + 3 = 0

To factorize this quadratic expression, we need to find two numbers whose product is 2 * 3 = 6 and whose sum is 5.

The numbers that fulfill these conditions are 2 and 3.

So we can rewrite the equation as follows by splitting the middle term:

2c^2 + 2c + 3c + 3 = 0

Now, factor by grouping:

(2c^2 + 2c) + (3c + 3) = 0

Take out the common factors:

2c(c + 1) + 3(c + 1) = 0

Notice that we have a common factor of (c + 1), so we can simplify further:

(2c + 3)(c + 1) = 0

We set each factor equal to zero:

2c + 3 = 0 or c + 1 = 0

Solving for c in each equation:

2c = -3 or c = -1

Dividing both sides of the first equation by 2:

c = -3/2

Thus, the solutions to the quadratic equation 2c^2 + 5c + 3 = 0 are c = -3/2 and c = -1.