Mathematics: What are the solutions of the equation? 5z^2-9z-2=0 a. -1,2 b. -1/5,-2 c. -1,-2 d. 1-/5,2

What are the solutions of the equation? 5z^2-9z-2=0

mikestarjo2173

09.03.2022

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 .

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