Answer: The correct options are
(B) [tex]x=-\dfrac{5}{3}[/tex]
(C) [tex]x=\dfrac{1}{2}.[/tex]
Step-by-step explanation: We are given to find the solutions to the following quadratic equation :
[tex]6x^2+7x-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We need to find two integers with sum 7 and product -30.
The solution of equation (i) is as follows :
[tex]6x^2+7x-5=0\\\\\Rightarrow 6x^2+(10-3)x-5=0\\\\\Rightarrow 6x^2+10x-3x-5=0\\\\\Rightarrow 2x(3x+5)-1(3x+5)=0\\\\\Rightarrow (2x-1)(3x+5)=0\\\\\Rightarrow 2x-1=0,~~~~~3x+5=0\\\\\Rightarrow x=\dfrac{1}{2},-\dfrac{5}{3}.[/tex]
Thus, the required solutions of the given equation are [tex]x=\dfrac{1}{2},-\dfrac{5}{3}.[/tex]
Options (B) and (C) are CORRECT.
