What substitution should be used to rewrite 4x⁴ - 21x² + 20 = 0 as a quadratic equation?
u = x²
u = 2x²
u = x⁴
u = 4x⁴

Solution:

It is given that

4x⁴ - 21x² + 20 = 0

The leading term is of power 4. To solve it quickly, we can substitute u = x² and rewrite it as a quadratic equation

4u² - 21u + 20 = 0

Using the formula x = [-b ± √(b² - 4ac)]/2a

Substituting the values

x = [-(-21) ± √((-21)² - 4(4)(20))]/2(4)

x = [21 ± √(441 - 320)]/ 8

x = [21 ± √121]/8

x = (21 ± 11)/8

So we get

x = (21 + 11)/ 8 and x = (21 - 11)/8

x = 32/8 and x = 10/8

x = 4 and x = 5/4

And the roots of the original equation are √4 and √(5/4) = 2, -2, √5/2, -√5/2

Therefore, u = x² substitution should be used to rewrite 4x⁴ - 21x² + 20 = 0 as a quadratic equation.

What substitution should be used to rewrite 4x⁴ - 21x² + 20 = 0 as a quadratic equation?
u = x²
u = 2x²
u = x⁴
u = 4x⁴

Summary:

The substitution that should be used to rewrite 4x⁴ - 21x² + 20 = 0 as a quadratic equation is u = x².