Which quadratic equation is equivalent to (x² - 1)² - 11(x² - 1) + 24 = 0?

Solution:

The question is based on the standard form of a quadratic equation.

Let's write the equation in it's standard form.

(x² - 1)² - 11(x² - 1) + 24 = 0

Consider (x² - 1) as u

u² - 11u + 24 = 0

u² - 8u  - 3u + 24 = 0

u(u - 8) - 3( u - 8)  = 0  → by splitting the middle term

(u - 8) ( u - 3)  = 0

(x² - 1 - 8 )( x² - 1 - 3) = 0   ---------> by putting (x² - 1) = u

(x² - 9 )( x² - 4) = 0

Hence, x² – 9 = 0 or x² – 4 = 0    -----> [ similar to the quadratic equation ax² + bx + c = 0 ]

Thus, (x² - 9) = 0 or (x² - 4) = 0 are the standard form of (x² - 1)² - 11(x² - 1) + 24 = 0.

Which quadratic equation is equivalent to (x² - 1)² - 11(x² - 1) + 24 = 0?

Summary:

(x² - 9) = 0 or (x² - 4) = 0 are the standard equivalent form to (x² - 1)² - 11(x² - 1) + 24 = 0.