Question

Find the solutions to the equation below check all that apply

Answer 1

the answers are x = 1/2 and x = -5/3. I hope this helped you, have a great day.

Answer 2

Answer:  The correct options are

(B) $x=-\dfrac{5}{3}$

(C) $x=\dfrac{1}{2}.$

Step-by-step explanation:  We are given to find the solutions to the following quadratic equation :

$6x^2+7x-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We need to find two integers with sum 7 and product -30.

The solution of equation (i) is as follows :

$6x^2+7x-5=0\\\\\Rightarrow 6x^2+(10-3)x-5=0\\\\\Rightarrow 6x^2+10x-3x-5=0\\\\\Rightarrow 2x(3x+5)-1(3x+5)=0\\\\\Rightarrow (2x-1)(3x+5)=0\\\\\Rightarrow 2x-1=0,~~~~~3x+5=0\\\\\Rightarrow x=\dfrac{1}{2},-\dfrac{5}{3}.$

Thus, the required solutions of the given equation are $x=\dfrac{1}{2},-\dfrac{5}{3}.$

Options (B) and (C) are CORRECT.