The solutions to the given equation will be two distinct rational solutions, i.e. option A.
Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
[tex]2x ^2 -5=3x[/tex]
Now,
Rearrange the equation,
[tex]2x ^2 -3x-5=0[/tex]
Now,
Using the mid term splitting method,
[tex]2x ^2 -3x-5=0[/tex]
i.e.
[tex]2x ^2 -5x+2x-5=0[/tex]
Now,
Taking common,
[tex]2x ^2 +2x-5x-5=0[/tex]
i.e.
[tex]2x (x +1)-5(x+1)=0[/tex]
We get,
[tex](x +1)(2x -5)=0[/tex]
Now,
(x +1) = 0
⇒ x = -1
Now,
(2x -5 )= 0
⇒ [tex]x =\frac{5}{2} =2.5[/tex]
So, the solutions of the given equation are -1 and 2.5.
Hence, we can say that the solutions to the given equation will be two distinct rational solutions, i.e. option A.
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