Question

Which quadratic equation is equivalent to (x^2-1)^2-11(x^2-1)+24=0?

a) u^2-10u+24=0, where (u=x^2-1)
b) 42^2-11(42)+24=0 , where u=(x^2−1)
c) u^2+1-110+24=0, where u=(x^2−1)
d) (u^2-1)^2−11(u^2−1)+24=0 where u=(x^2−1)

Answer 1

The equivalent quadratic equation to the given expression (x^2-1)^2-11(x^2-1)+24=0 is u^2-11u+24=0, where u=x^2-1, which corresponds to option a.

Step-by-step explanation:

The quadratic equation given is (x^2-1)^2-11(x^2-1)+24=0. To find an equivalent quadratic equation, we can use a substitution method where we let u be equal to x^2 - 1. This simplifies the original equation to one in terms of u:

u^2 - 11u + 24 = 0.

Comparing this with the given options, we conclude that option a is the equivalent quadratic equation because if we substitute u with x^2 - 1, we get back the original equation. So the correct quadratic equation is u^2 - 11u + 24 = 0, where u = x^2 - 1.