Final answer:
The value for the constant c that makes z = -5/4 an extraneous solution in the equation √(4z + 9) = cz + 8 is c = -24/5.
Step-by-step explanation:
To determine the value for the constant c that makes z = -5/4 an extraneous solution in the equation √(4z + 9) = cz + 8, we substitute the value of z into the equation and solve for c.
Substituting z = -5/4 into the equation:
√(4(-5/4) + 9) = c(-5/4) + 8
√(-5 + 9) = (-5/4)c + 8
√(4) = (-5/4)c + 8
2 = (-5/4)c + 8
(-5/4)c = 2 - 8
(-5/4)c = -6
c = -6 * (4/5) = -24/5
Therefore, the value for the constant c that makes z = -5/4 an extraneous solution in the given equation is c = -24/5.