Question

Select the two values of x that are roots of this equation.

2x-5=-3x^2
A. x= 3
B. X=1
C. x=-5/3
D. x=-1/2

Answer 1

`\large\boxed{B.\ x=1,\ C.\ x=-(5)/(3)}`

Explanation:

`2x-5=-3x^2\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2+2x-5=0\\\\3x^2+5x-3x-5=0\\\\x(3x+5)-1(3x+5)=0\\\\(3x+5)(x-1)=0\iff3x+5=0\ \vee\ x-1=0\\\\3x+5=0\qquad\text{subtract 5 from both sides}\\3x=-5\qquad\text{divide both sides by 3}\\x=-(5)/(3)\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1`