Question

Which describes the solution set of (5x –1)(x + 2) = 8x – 4?

the equation has one real solution x=-1/5
the equation has no real solution
the equation has two real solutions x=0 x=-5
the equation has two real solutions x=1 x= -1/5

Answer 1

(5x-1)(x+2)=8x-4
5x²+10x-x-2=8x-4
5x²+9x-2=8x-4
5x²+x+2=0
use the quadratic formula, b²-4ac=1²-4*5*2=1-40=-39, -39 cannot be square rooted, so the equation has no real solution.