Question

What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic equation

Answer 1

4y^2 - 21y + 20 = 0

Explanation:

As (4x^4 - 21x^2 + 20=0) being a biquadratic equation, meaning it is a 4-degree equation without the terms of degree 1 and 3.

To solve this particular case you only need to replace the variables of degree 4 and 2 for a new variable of degree 2 and 1 and solve it as regular quadratic equation and then undo the change.

* Using a new variable we can rewrite the equation:

Let y be the new variable;

y= x^2, then y^2= x^4

Then we have;

4y^2- 21y+20=0

Solve for y and then find X which will be the roots for the biquadratic equation.

Answer 2

let y = x^2

4y^2 -21y + 20 = 0

solve for y

then substitute back in to get x