Solve and check your solution(s). If the equation has no real solution, so state.
-
A) 3
B) -3, 1
C) 3, -1
D) no real solution

Question

Solve and check your solution(s). If the equation has no real solution, so state.
-
A) 3 
B) -3, 1 
C) 3, -1 
D) no real solution

Quizplus · Accepted Answer

To solve the equation, we need to set it equal to zero and factor:
$$4x^2-4x-3=0$$
$$(2x-3)(2x+1)=0$$
Using the zero product property, we have:
$$2x-3=0 \quad 	ext{or} \quad 2x+1=0$$
Solving for x, we have:
$$2x=3 \quad 	ext{or} \quad 2x=-1$$
$$x=\frac{3}{2} \quad 	ext{or} \quad x=-\frac{1}{2}$$
So the solution set is $\{3/2,-1/2\}$, which corresponds to choice C). To check our solution, we can plug each value back into the original equation to make sure it equals zero. We find that both choices satisfy the equation, so we can be confident in our answer.

Solve and Check Your Solution(s)