Question

Determine if the following sets of quadratics are equivalent.

a) (x^2 - 10x + 14 = 0) and ((2x - 10)^2 = 156)
b) (x - 10)^2 = 68) and (x^2 - 20x = -32)
c)( x^2 - 6x = 247) and ((x - 3)^2 = 256)
d)(( x + 5)^2 = 65) and (x^2 = 90 - 10x)

Answer 1

To determine if the sets of quadratics are equivalent, we compare their coefficients and constant terms. Set (c) is equivalent, while the other sets are not.

Step-by-step explanation:

To determine if the sets of quadratics are equivalent, we need to compare the coefficients and constant terms of the quadratic equations. Let's analyze each set:

1. a) (x^2 - 10x + 14 = 0) and ((2x - 10)^2 = 156)

   These two quadratics are not equivalent because their coefficients and constant terms are not the same.

2. b) (x - 10)^2 = 68) and (x^2 - 20x = -32)

   These two quadratics are not equivalent because their coefficients and constant terms are not the same.

3. c) (x^2 - 6x = 247) and ((x - 3)^2 = 256)

   These two quadratics are equivalent because their coefficients and constant terms are the same.

4. d) ((x + 5)^2 = 65) and (x^2 = 90 - 10x)

   These two quadratics are not equivalent because their coefficients and constant terms are not the same.