Question

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

Answer 1

The answer should be U=X^2

Answer 2

We can substitute t = x² to make the given equation quadratic.

Explanation:

The given equation is,

`4x^4-21x^2+20=0`

This is a polynomial equation of degree 4.

The standard form of a quadratic equation is,

`ax^2+bx+c=0`

The given equation can be written as,

`4(x^2)^2-21x^2+20=0`

Substitute x² = t,

`4(t)^2-21t+20=0`

This a quadratic equation because the degree of the equation is 2.