Question

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

Answer 1

Option (D) is correct.

The solution of the quadratic equation
`5z^2-9z-2=0` is
`(-1)/(5)` and
`z=2`.

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=(-1)/(5)` or
`\Rightarrow z=2`

Thus, the solution of the quadratic equation
`5z^2-9z-2=0` is
`(-1)/(5)` and
`z=2`.