Question

What are the solutions of the equation?

Answer 1

Answer:

c. 1/5, -2

Step-by-step explanation:

We are given the following equation and we are to solve it by factorizing it:

$5z^2 + 9z - 2 = 0$

We are to find factors of -10 such that when multiplied they give a product of -10 and when added they give a result of 9.

$5z^2 - z + 10z - 2 = 0$

$z (5z-1) + 2(5z-1) = 0$

$(z+2)(5z-1)=0$

$z=-2, z= \frac{1}{5}$

Therefore, the correct answer option is c. 1/5, -2.

Answer 2

Answer:

$\frac{1}{5},-2$

Step-by-step explanation:

We are given an equation 5z² + 9z - 2 = 0 and we are to find possible values of z by solving that equation

We will do the task by factorization method:

5z² + 9z - 2 = 0

We can break the midterm (+9z) in two terms such that when they are multiplied the result is -10z² i.e. equal to product of first and third term of the equation above and their sum is equal to 9z

5z² + 10z - z - 2 = 0

5z(z + 2) - 1(z + 2) = 0

taking z+2 common in the above equation

(z+2)(5z-1) = 0

We can write above equation as

(x+2) = 0                  (5z-1) = 0

x = -2;                       5z = 1

                                 $z=\frac{1}{5}$

$z=\frac{1}{5},-2$