Answer:
Option (D) is correct.
The solution of the quadratic equation [tex]5z^2-9z-2=0[/tex] is [tex]\frac{-1}{5}[/tex] and [tex]z=2[/tex].
Step-by-step explanation:
Consider the given quadratic equation [tex]5z^2-9z-2=0[/tex]
We can solve a quadratic equation using middle term splitting method,
-9z can be written as -10z+z
thus, the equation becomes,
[tex]5z^2-10z+z-2=0[/tex]
Taking factors common, we get,
[tex]\Rightarrow 5z(z-2)+1(z-2)=0[/tex]
[tex]\Rightarrow (5z+1)(z-2)=0[/tex]
[tex]\Rightarrow (5z+1)=0[/tex] or [tex]\Rightarrow (z-2)=0[/tex]
[tex]\Rightarrow z=\frac{-1}{5}[/tex] or [tex]\Rightarrow z=2[/tex]
Thus, the solution of the quadratic equation [tex]5z^2-9z-2=0[/tex] is [tex]\frac{-1}{5}[/tex] and [tex]z=2[/tex].
