Question

What are the solutions of the equation?

Answer 1

Answer:

Option (D) is correct.

The solution of the quadratic equation $5z^2-9z-2=0$ is $\frac{-1}{5}$ and  $z=2$.

Step-by-step explanation:

Consider the given quadratic equation $5z^2-9z-2=0$

We can solve a quadratic equation using middle term splitting method,

-9z can be written as -10z+z

thus, the equation becomes,

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

Taking factors common, we get,

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

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

$\Rightarrow (5z+1)=0$  or  $\Rightarrow (z-2)=0$

$\Rightarrow z=\frac{-1}{5}$ or $\Rightarrow z=2$

Thus, the solution of the quadratic equation $5z^2-9z-2=0$ is $\frac{-1}{5}$ and  $z=2$.