What substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation?


Asked by maham237 @ in Mathematics viewed by 356 People

Answered by maham237 @



Answer:

The substitution is

u = x ^ 4

u ^ 2 -3u +2 = 0

Step-by-step explanation:

We have the 8th degree polynomial equation

x ^ 8 - 3x^4 -+2 = 0

To rewrite the equation as a quadratic function, take the common factor of the term x with the smallest exponent, in this case it is x ^ 4.

Now make a change of variable

u = x ^ 4.

So rewriting the equation in terms of u, we have:

u ^ 2 -3u +2 = 0

Now the initial equation became a quadratic equation

Factoring is left:

(u-2) (u-1) = 0

u = 2 and u = 1

x ^ 4 = 2 and x ^ 4 = 1


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