Question

1. Solve.

a) (x + 5)(x + 2) = 0
b) (x − 3)(x + 4) = 0
c) (x − 1)(x − 7) = 0
d) x(x + 9) = 0
e) (2x + 3)(x - 5) = 0
f) (2x − 1)(3x + 4) = 0
g) (3x - 5)(4x - 3) = 0 ​

Answer 1

To solve each quadratic equation, use the zero product property. Set each factor equal to zero and solve the resulting equations to find the solutions.

Step-by-step explanation:

To solve these quadratic equations, we can use the zero product property. This property states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

1. For equation (a), we have (x + 5)(x + 2) = 0. Setting each factor equal to zero, we find x + 5 = 0 or x + 2 = 0. Solving these equations, we get x = -5 or x = -2.
2. For equation (b), we have (x - 3)(x + 4) = 0. Setting each factor equal to zero, we find x - 3 = 0 or x + 4 = 0. Solving these equations, we get x = 3 or x = -4.
3. For equation (c), we have (x - 1)(x - 7) = 0. Setting each factor equal to zero, we find x - 1 = 0 or x - 7 = 0. Solving these equations, we get x = 1 or x = 7.
4. For equation (d), we have x(x + 9) = 0. Setting each factor equal to zero, we find x = 0 or x + 9 = 0. Solving these equations, we get x = 0 or x = -9.
5. For equation (e), we have (2x + 3)(x - 5) = 0. Setting each factor equal to zero, we find 2x + 3 = 0 or x - 5 = 0. Solving these equations, we get x = -3/2 or x = 5.
6. For equation (f), we have (2x - 1)(3x + 4) = 0. Setting each factor equal to zero, we find 2x - 1 = 0 or 3x + 4 = 0. Solving these equations, we get x = 1/2 or x = -4/3.
7. For equation (g), we have (3x - 5)(4x - 3) = 0. Setting each factor equal to zero, we find 3x - 5 = 0 or 4x - 3 = 0. Solving these equations, we get x = 5/3 or x = 3/4.