Problem:
If the expression
∣∣∣∣∣adcb∣∣∣∣∣
has the value ab−cd for all values of a,b,c and d, then the equation
∣∣∣∣∣2xx1x∣∣∣∣∣=3
Answer Choices:
A. is satisfied for only 1 value of x.
B. is satisfied for 2 values of x.
C. is satisfied for no values of x.
D. is satisfied for an infinite number of values of x.
E. is satisfied for none of these answers.
Solution:
Solving for x:
∣∣∣∣∣2xx1x∣∣∣∣∣(2x)(x)−(1)(x)2x2−x−3(2x−3)(x+1)=3=3=0=0
Setting the factors to zero gives two distinct real solutions: x=−1 and x=23.
Since the equation is satisfied for exactly 2 values of x, the correct choice is B.